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Point P is 40 mm and 30 mm from horizontal and vertical axes respectively draw Hyperbola through it

Engineering Graphics-1 : Question Paper Dec 2015 - First

  1. Draw its projections. (13 marks) 4 (a) Point P is 40 mm and 30 mm from horizontal and vertical axes respectively. Draw Hyperbola through it. (7 marks) 4 (b) A right circular cone of base diameter 50 mm and axis height 60 mm has it is base in horizontal plane. Draw the development of the lateral surface of cone. (6 marks
  2. Problem No.10: Point P is 40 mm and 30 mm from horizontal HYPERBOLAand vertical axes respectively.Draw Hyperbola through it. THROUGH A POINT OF KNOWN CO-ORDINATES Solution Steps: 1) Extend horizontal line from P to right side
  3. 4 Point P is 40 mm and 30 mm from horizontal and vertical axes respectively. Draw Hyperbola through it. (Nov 2015, 7M) d) RECTANGULAR HYPERBOLA 1 A point P is 25 mm and 35 mm from two straight lines are at right angles to each other, Construct a rectangular hyperbola. E) INVOLUTE 1 Draw an involute of a circle of 40 mm diameter for one convolution
  4. Point P is 40 mm and 30 mm from horizontal and vertical axes respectively. Draw Hyperbola through it. [71 A right circular cone of base diameter 50 mm and axis height 60 mm has it is base in horizontal plane. Draw the development of the lateral surface of cone. [61 Using first angle method, draw the following views for the object shown in Fig.
  5. HYPERBOLA Problem No.10: Point P is 40 mm and 30 mm from horizontal and vertical axes respectively.Draw Hyperbola through it. THROUGH A POINT OF KNOWN CO-ORDINATES Solution Steps: 1) Extend horizontal line from P to right side. 2) Extend vertical line from P upward
  6. Problem No. 10: Point P is 40 mm and 30 mm from horizontal and vertical axes respectively.Draw Hyperbola through it. HYPERBOLA THROUGH A POINT OF KNOWN CO-ORDINATES Solution Steps: 1) Extend horizontal line from P to right side. 2) Extend vertical line from P upward
  7. HYPERBOLA. Problem No.10: Point P is 40 mm and 30 mm from horizontal and vertical axes respectively.Draw Hyperbola through it. THROUGH A POINT OF KNOWN CO-ORDINATES. Solution Steps: 1) Extend horizontal line from P to right side. 2) Extend vertical line from P upward

Unit 1 engineering curves - SlideShar

  1. P O 40 mm 30 mm 1 2 3 2 1 11,2,3,4 draw vertical 2 3 1 2 HYPERBOLA THROUGH A POINT OF KNOWN CO-ORDINATES Solution Steps: 1) Extend horizontal line from P to right side. 2) Extend vertical line from P upward. 3) On horizontal line from P, mark some points taking any distance and name them after P-1, 2,3,4 etc. 4) Join 1-2-3-4 points to pole O
  2. P-B] draw horizontal lines. 7Line from 1 horizontal and line from 1 vertical will meet at P 1.Similarly mark P 2, P 3, P 4 points. 8Repeat the procedure by marking four points on upward vertical line from P and joining all those to pole O. Name this points P 6, P 7, P 8 etc. and join them by smooth curve. Problem: Point P is 40 mm and 30 mm.
  3. 8) Repeat the procedure by marking four points on upward vertical line from P and joining all those to pole O. Name this points P6 , P7 , P8 etc. and join them by smooth Problem No.10: Point P is 40 mm and 30 mm from horizontal and vertical axes respectively.Draw Hyperbola through it. 18. Problem 14: Two points A and B are 50 mm apart

Curve1 - slideshare

  1. 8) Repeat the procedure by marking four points on upward vertical line from P and joining all those to pole O. Name this points P6, P7, P8 etc. and join them by smooth curve. Problem No.10: Point P is 40 mm and 30 mm from horizontal and vertical axes respectively.Draw Hyperbola through it. 46
  2. There is a point P, moving in a plane such that the difference of it's distances from A and B always remains constant and equals to 40 mm. Draw locus of point P. Basic Locus Cases: Solution Steps: 1.Locate A & B points 100 mm apart. 2.Locate point P on AB line, 70 mm from A and 30 mm from B As PA-PB=40 ( AB = 100 mm ) 3.On both sides of P.
  3. Y. B. Tech. PROBLEM : Point F is 40 mm from a vertical Straight line AB. Draw locus of point P, moving in a plane such That it always remains equidistant from point F and line AB. Draw tangent and normal at a point S lying on a curve below the axis at a distance of 55 mm from the lin
  4. from line AB and fixed point F. Problem No.10: Point P is 40 mm and 30 mm from horizontal HYPERBOLA and vertical axes respectively.Draw Hyperbola through it. THROUGH A POINT OF KNOWN CO-ORDINATES Solution Steps: 1) Extend horizontal line from P to right sid
  5. PARABOLA SOLUTION STEPS: 1.Locate center of line, perpendicular to A AB from point F. This will be initial point P and also the vertex. 2.Mark 5 mm distance to its right side, name those points 1,2,3,4 and from P1 those draw lines parallel to AB. 3.Mark 5 mm distance to its left of P and (VERTEX) V name it 1

Problem No.10: Point P is 40 mm and 30 mm from horizontal and vertical axes respectively.Draw Hyperbola through it. SSolution Steps: HYPERBOLA Extend horizontal line from P to THROUGH A POINT right sid Ifthe vertical distance between the orifice and the point is 30 em, draw the path of the jet of water.Hyperbola 1. A vertex of a hyperbola is 50 mm from its focus. Draw two parts of the hyperbola; if the eccentricity is 3/2. 2. Two fixed point A and Bare 120 mm apart PROBLEM 12:-POINT F IS 50 MM FROM A LINE AB.A POINT P IS MOVING IN A PLANE SUCH THAT THE RATIO OF IT'S DISTANCES FROM F AND LINE AB REMAINS CONSTANT AND EQUALS TO 2/3 DRAW LOCUS OF POINT P. { ECCENTRICITY = 2/3 } STEPS: 1 .Draw a vertical line AB and point F 50 mm from it. 2 .Divide 50 mm distance in 5 parts. 3 .Name 2nd part from F as V. It.

ENGINEERING DRAWING _ I

7) Line from 1 horizontal and line from 1 vertical will meet at P 1.Similarly mark P 2, P 3, P 4 points. 8) Repeat the procedure by marking four points on upward vertical line from P and joining all those to pole O. Name this points P 6, P 7, P 8 etc. and join them by smooth curve. Problem No. 08: Point P is 40 mm and 30 mm from horizontal and. 1)Point P is 130 mm away from the fixed point pole O. The point P moves towards pole O and reaches the position P' in one convolution, where OP' is 22 mm. The point P moves in such a way that its movement towards fixed point O, being uniform with its movement around fix point pole O. Draw the curve traced out by the point P. Name the curve PROBLEM 12:-POINT F IS 50 MM FROM A LINE AB.A POINT P IS MOVING IN A PLANE SUCH THAT THE RATIO OF IT'S DISTANCES FROM F AND LINE AB REMAINS CONSTANT AND EQUALS TO 2/3 DRAW LOCUS OF POINT P. { ECCENTRICITY = 2/3 } STEPS: 1 .Draw a vertical line AB and point F 50 mm from it. 2 .Divide 50 mm distance in 5 parts. 3 .Name 2nd part from F as V

Video: Engineering Graphics ED Ellipse Perpendicula

9. (a) The major and minor axis of an ellipse is 120&80 mm. Draw an ellipse by arcs of circles method. (b) The asymptotes of a hyperbola are inclined at 700 to each other. Construct the curve when a point p on it is at a distance of 20 mm and 30 mm from the two asymptotes. 10. Two fixed points A&B are 100 mm apart ellipse directrix-focus method problem 6:-point f is 50 mm from a line ab. a point p is moving in a plane such that the ratio of it's distances from f and line ab remains constant and equals to 2/3 draw locus of point p. { eccentricity = 2/3 } f ( focus) v ellipse (vertex) a b steps: 1 .draw a vertical line ab and point f 50 mm from it 1.a) A point P is 30 mm and 50 mm respectively from two straight lines which are at right angles to each other. Draw a rectangular hyperbola from P within 10 mm distance from each line. b) Draw a vernier scale of R.F. = 1/25 to read centimeters upto 4 metres and on it, show lengths representing 2.39 m and 0.91 m. [8+7] O View Engineering Curves PPT Naman Dave-1_1429898310912.pptx from MECHANICAL 123 at Gayatri Vidya Parishad College of Engineering. This file conduct some of your problems from your manual, wit

f ( focus) v (vertex) a b 30mm hyperbola directrix focus method problem 12:- point f is 50 mm from a line ab.a point p is moving in a plane such that the ratio of its distances from f and line ab remains constant and equals to 2/3 draw locus of point p. { eccentricity = 2/3 } steps: 1 .draw a vertical line ab and point f 50 mm from it

BE sem 1 Engineering Graphics(E

A point P is 29 mm above the HP and 22 mm behind the VP while a point Q is 40 mm below HP and 30 mm in front of VP. Draw the projection of the line and determine the true length and the true inclinations with the HP and VP. 8. The end of a line PQ is on the same projector. The end P is 30 mm below H.P. and 12 mm behind V.P 5. Draw a hyperbola when the distance between the focus and directrix is 40 mm and the eccentricity is 4/3. Draw a tangent and normal at any point on the hyperbola. b) CYCLOIDS & INVOLUTES. 6. Draw the involute of a square of side 30 mm. Also draw tangent and normal to the curve from any point on it. 7. A coir is unwound from a drum of 30mm. A point P on the curve is at a distance of 40 mm from the horizontal asymptote and 50 mm from the inclined asymptote. Plot the curve. Draw a tangent and normal to the curve at any point M. 5 4. Draw the locus of a point P moving so that the ratio of its distance from a fixed point F to its distance from a fixed straight line DD' is 1. Also draw tangent and normal to the curve from any point on it. 5. Draw a hyperbola when the distance between the focus and directrix is 40 mm and the eccentricity is 4/3

6. Construct a parabola when the distance between focus and the dicretrix is 40 mm. Draw tangent and normal at any point P on your curve. 7. A fixed point F is 7.5cm from a fixed straight line. Draw the locus of a point P moving in such a way that its distance from the fixed straight line is equal to its distance from F. Name the curve Draw a path of a ball which is thrown from ground level which reaches a height of 30 m and a horizontal distance of 60 m before return to the ground. Name the curve. 10. Draw the hyperbola when its vertex and its focus are at a distance of 40 mm and 25 mm respectively from the directrix

Mechanical Drafting (Engineering Drawing)- Complete syllabu

How to draw tangent and normal to Epicycloid here the

Academia.edu is a platform for academics to share research papers PROBLEM :-1. Three points A, B & P while lying along a horizontal line in order have AB = 60 mm and AP = 80 mm, while A & B are fixed points and P starts moving such a way that AP + BP remains always constant and when they form isosceles triangle, AP = BP = 50 mm. Draw the path traced out by the point P from the commencement of its motion back to its initial position and name the path of P

Engineering Grpaphics-1 Ellipse Circl

(PPT) Engineering Graphics Rajesh Gaikwad - Academia

Draw a circle of radius 55 which connects tangentially both the circles and (a) include 20 mm circle (b) include 30 mm circle. 3.17 A point P is 40 mm from a line AB. Another point Q is in the AB and is 50 mm from the point P. Draw a circle passing through point P and tangential to the line AB at point Q. 3.18 Draw two possible circles to. Divide vertical small side and horizontal long side into same number of equal parts.( here divided in four parts) Step 3. Now join all vertical points 1,2,3,4, to the upper end of minor axis. And all horizontal points i.e.1,2,3,4 to the lower end of minor axis. Step 4. Then extend D-1 line upto C-1 and mark that point A vertical cylinder with a 60 mm diameter is penetrated by a horizontal square prism with a 40 mm base side, the axis of which is parallel to the VP and 10 mm away from the axis of the cylinder. A face of the prism makes an angle of 30° with the HP. Draw their projections showing curves of intersection. Intersection of Cylinder and Con Find the length of the major or minor axes of an ellipse - Examples. Let us see some example problems based on the above concept. Example 1 : Find the length of major and minor axes of the following ellipse. x ²/9 + y ²/4 = 1. Solution : To find the length of major and minor axis, first we have to find the length of a and b

Curves 1 Ellipse Perpendicula

(iii) Arc of circle method. Draw a tangent and normal to the ellipse at a point on it 40 mm above the major axis. 14. Two fixed points A and B are 100 mm apart. Trace the complete path of a point P moving (in the same plane as that of A and B) in such a way that sum of its distance . Curve1 - SlideSha 3.17 Draw the projections of a circle of 50 mm diameter resting in the horizontal plane on a point A on the circumference, its plane inclined at 45˚ to the H.P. and the top view of the diameter AB making 30˚ angle with the V.P. (W02) Solution: A hexagonal prism of base side 30 mm and axis length 70 mm rests on one of its ends on the H.P. with two base sides parallel to the V.P. It is cut by a plane perpendicular to the V.P. and inclined at 300 to the H.p. The cutting plane meets the axis at 30 mm from the top. Draw the front view, sectional top view and the true shape Of the section Smax = 69.1 mm I =0 with a speed of 40 km/h. It then undergoes an acceleration which varies with displacement as shown. (-8) 2 = 17.89 m/s 2 u= \ 3 j (-30)2 + (-40)2 Helpful Hint The velocity and acceleration components and their resultants are shown on the separate diagrams for point A, where y = 0. '' 2/ 69 A long jumper approaches. A POINT P IS MOVING IN A PLANE SUCH THAT THE RATIO OF ITS DISTANCES FROM F AND LINE AB REMAINS CONSTANT AND EQUALS TO 2/3 DRAW LOCUS OF POINT P. { ECCENTRICITY = 2/3 } STEPS: 1 .Draw a vertical line AB and point F 50 mm from it. 2 .Divide 50 mm distance in 5 parts. 3 .Name 3rd part from F as V. It is 30 mm and 20 mm from F and AB line resp

TEXTBOOK OF ENGINEERING DRAWING Pages 101 - 150 - Flip PDF

The x-axis could be chosen to point straight downward or to some other logical direction. The origin should be chosen based on the problem statement. Note that this puts the z-axis in a horizontal orientation, which is a little different from what we usually do. It may make sense to choose an unusual orientation for the axes if it makes sense. In the case of Figure 1 the horizontal and vertical axes represent the variables x and y, respectively, so they are labelled accordingly, and may be referred to as the x-axis and the y-axis. If we were to use the axes to represent two different variables, say m and t, then they would be known as the m-axis and the t-axis

O P 1 P 2 12 1302013 3 P O 40 mm 30 mm 1 2 3 1 2 1 2 3 1 2

8) Repeat the procedure by marking four points on upward vertical line from P and joining all those to pole O. Name this points P6, P7, P8 etc. and join them by smooth curve. Problem No.10: Point P is 40 mm and 30 mm from horizontal and vertical axes respectively.Draw Hyperbola through it * LOCATE POINT Q AS DISCRIBED IN PROBLEM AND THROUGH IT DRAW A TANGENTTO THIS SMALLER CIRCLE.THIS IS A NORMAL TO THE SPIRAL. *DRAW A LINE AT RIGHT ANGLE *TO THIS LINE FROM Q. IT WILL BE TANGENT TO CYCLOID. Point P is 40 mm and 30 mm from horizontal and vertical axes respectively.Draw Hyperbola through it. VOLUME:( M3 ) PRESSURE ( Kg/cm2) 0. Methods of Drawing Tangents & Normals To These Curves. ENGINEERING CURVES Part- I {Conic Sections}. PARABOLA 1.Rectangle Method 2 Method of Tangents ( Triangle Method) 3.Basic Locus Method (Directrix - focus). ELLIPSE 1.Concentric Circle Method 2.Rectangle Method.. A point 30 mm above x y line is the plan-view of two points P and Q. The elevation of P is 45 mm above the HP while that of Q is 35 mm below HP. Draw the projections of the points and states their position with reference to the principal planes and the quadrant in which they lie Engineering Graphics. INDEX. Introduction Scales Engineering Curves Orthographic Projection Isometric Projection Projection of Points & Lines Projection of Planes Projection of Solids Section of Solids. TYPES OF LINES. DIMENSIONS OF LARGE OBJECTS MUST BE REDUCED TO ACCOMMODATE Slideshow..

Scales, Curves,Basic concepts of Engineering Drawing

Solution: Isometric projection is useful for visually representing 3-D objects in two dimensions. Any other line which is not parallel to any of the isometric axes is known as Non-Isometric Line. 1. The lines XY, YZ & ZX are called non-isometric lines. Note: a-b and AB=ACMD. THrough O draw OP and OQ at 30º & 45º to the horizontal respectively The distance between plane P and the distal end of the ulna was represented by L. The horizontal and vertical components of the distance between the longitudinal axes of the forearm bones at plane P were represented by S and T respectively, and those at the point L/2 distal from plane P by M and N respectively A hexagonal prism I5 mm side of base and axis 60 mm rest with one of its rectangular faces on ground and axis being parallel to V.P. lt is cut by a section and inclined at 30° to the V.P. at a point I5 mm from one of its ends. Draw the sectional front view and the true shape of the section. 10. A pentagonal pyramid 30 mm side of base and axis. (A) The point through which the resultant of the shear stresses passes is known as shear centre (B) In the standard rolled channels, the shear centre is on the horizontal line passing through and away from the C.G. beyond web (C) In equal angles, the shear centre is on the horizontal plane and away from the C.G., outside of the leg projectio If point D is on the horizontal plane and 5 mm behind the vertical plane both, its plan is. 21. A point is 20 mm below HP and 30 mm behind VP. Its top view will be. The front view of a point is 40 mm above xy and the top view is 50 mm below xy, the

Draw a tangent and a normal to the curve at a point 70mm away from the fixed straight line. Draw rhombus of 100 mm & 70 mm long diagonals and inscribe an ellipse in it by four centre method. A rectangle has a sides PQ=12cm and QR=8cm.Inscribe a parabola passing through the point P and Q and the midpoint M of the side RS Head rotations about horizontal, vertical, and nasal-occipital axes produce VOR responses with horizontal, vertical and torsional counter-rotations of the slow phase of the nystagmus (Seidman and Leigh, 1989). Fig. 5 Vestibular end-organs in the human temporal bone. Three canals transduce angular head acceleration and two otoliths, the sacculus. (d) a hyperbola (iv) A fish which is at a depth of 12 cm in water (μ = 4/3) is viewed by an observer on the bank of a lake. Its apparent depth as observed by the observer is : (a) 3 cm (b) 9 cm (c) 12 cm (d) 16 cm (v) If Ep and Ek represent potential energy and kinetic energy respectively, of an orbital electron, then, according to Bohr's. The growth rates of the horizontal and vertical axes (rhizomes and shoots) were correlated. The mean internode length and the PIR were related. The correla- tion is best described by part of an hyperbola (Fig. 2) (r=0.62, P<0.01). A linear regression {line 2) (r=0.59, P<0.001) calculated a reduction in the mean internode length of 2 mm for. Step-1 Draw a horizontal major axis of the length 140 mm and give the notations A & B as shown in the figure. And mark a midpoint C on it. Step-2 Draw a vertical axis, perpendicular to the horizontal axis & passing through the point C; of the length equal to the length of minor axis, which is 100 mm and give the notations C & D as shown in the.

A straight line through the origin O meets the parallel lines 4x+2y=9 and 2x+y+6=0 at P and Q respectively. The point O divides the segment PQ in the ratio Let each of the equations x^2+2xy+ay^2=0 and ax^2+2xy+y^2=0 represent two straight lines passing through the origin - Selection from Engineering Drawing, 2nd Edition [Book] 30/60 degrees. Solution: Isometric projection is useful for visually representing 3-D objects in two dimensions. Or the isometric length is 0.816 of the actual length. THrough O draw OP and OQ at 30º & 45º to the horizontal respectively O Scribd é o maior site social de leitura e publicação do mundo

Engineering Drawing: UNIT_I - Engineering Curve

Provide HB 450,@0.925 kN/m with two plates 700 mm x 18 mm. One plate is connected with each flange of I-section. The design drawing is given in Fig. 10.8. Step 4. Area of plates. From IS:800-1984 for l/r=17.567 and the steel having yield stress, f y =260 N/mm 2, allowable working stress in compression σ ac =154.486 N/mm 2 (MPa An illustration of a horizontal line over an up pointing arrow. Upload. An illustration of a person's head and chest. Sign up | Log in. An illustration of a computer application window Wayback Machine. An illustration of an open book. Books. An illustration of two cells of a film strip.. A and B, weighing 40 lb and 30 lb, respectively, rest on smooth planes as shown in Fig. 5-6. They are connected by a weightless cord passing over a frictionless pulley. Determine the angle в and the tension in the cord for equilibrium. Fig. 5-6 40 lb 30 Ib («) ib) Fig. 5-7 SOLUTION Draw free-body diagrams of Fig. 5-7(я) and (b) Let us take an example: A composite rod is 1000 mm long, its two ends are 40 mm2 and 30 mm2 in area and length are 300 mm and 200 mm respectively. The middle portion of the rod is 20 mm2 in area. 4. Draw the locus of a point P moving so that the ratio of its distance from a fixed point F to. its distance from a fixed straight line DD' is 1. Also draw tangent and normal to the curve. from any point on it. 5. Draw a hyperbola when the distance between the focus and directrix is 40 mm and the

The average discharge per unit thickness of the layer is Q/b, and since the water flows into the well over its entire periphery, we have q= Q 2nb (5.36) 286 Thus, the potential function has the form: 5. GROUNDWATER FLOW = JjLln* and for r = rw, = 0. The stream function takes the form: (5.37) , -£· Geometric and Engineering Drawing 144 25 25 12. 5 12. 5 12. 5 12. 5 75 75 60° 45° Dimensions in mm P Figure 10 30° 38 mm X X Figure 11 9. Figure 9 shows a church steeple which is square in plan, to a scale of 1:100 draw: (a) a front elevation; (b) a sectional plan on a cutting plane 2600mm above the centre of the clock. Ignore the chain lines It is therefore the equation of the line. Likewise, a line parallel to P ~ ^ the y-axis has an equation of X the form x= c. (2) The line not parallel to an axis. Fie, 61. Let the line cut the y-axis at N(O, b). Let P(x, y) be any point of the line. Through P draw PM parallel to the x-axis to meet the y-axis in I Enter the horizontal and vertical distances as 50 mm, in the Cartesian tab of the Circle Definition dialog box. (30, 30) to a second point (40, 40) through which the circle will pass (Figure 2.

I l/ and (12), respectively. We draw lines from the left end- points of L and M through B, and from the right endpoints of L and M through C. These lines are extended until they intercept the cos and sin axes. respectively. The part of the axes between the in- tercepts determines the mobility range of link I in terms of sin 0 and cos 0 In mathematics, an ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant.As such, it generalizes a circle, which is the special type of ellipse in which the two focal points are the same.The elongation of an ellipse is measured by its eccentricity, a number ranging from = (the limiting case. Tangent And Normal to A Hyperbola 9. Mark a point P on the hyperbola at a given distance, 30 mm from the directrix. 10. Join PF. 11. Draw a line FT perpendicular to PF F meeting directrix at T. 12. Join TP and extend it to some point T ′. The line TT ′ is the required tangent. 13. Through point P, draw a line NN ′ perpendicular to TT ′ Suppose v is the position vector OP of the point P. and Mv is the position vector of the point P'. Then you can say that P maps onto point P' under the transformation defined by the matrix M, or M.

Elipse,Parabola,Hyperbola Drawings

The position of a point in a plane can also be determined with reference to two axes that are not at right angles; but the angle o between these axes must be given (Fig. 6). The abscissa and the ordinate of the point P are then y/ the segments OQ=x, OR=y cut off on Q the axes by the parallels through P to the FIG. C axes C O N I C S E C T I O N S Section Plane Through Generators Section Plane Parallel to end generator. Section Plane Parallel to Axis. These are the loci of points moving in a plan find a function f given that (1) the slope of the tangent line to graph of f at any point P(x,y) is given by dy/dx=3xy and (2) the graph of f passes through the point (0,2) elect and magn. a postive charge of q is located at x=0 and y=-a, and a negative charge -q is located at the point x=0 and y=+a

t 0 = 15sin37 × 6 + 20 sin 30° × 4 - 10 × 4 = 54 + 40 - 40 = 54 N-cm. t 0 = 0.54 N-m Ex.16 A particle having mass m is projected with a velocity v 0 from a point P on a horizontal ground making an angle q with horizontal. Find out the torque about the point of projection acting on the particle whe Take any point as D on the hyperbola of which CA is the semi- D major axis, and through this point B draw the tangent D Tand the semidiameter CD, also take any other point, as P, on the curve, and draw C Lt m G the tangent Pt, the ordinate PHto the diameter through D, and the ordinates PQ and DG to the axis Problem: Draw an ellipse by general method, given distance of focus from directrix 50 mm and eccentricity 2/3. Also draw normal and tangent on the curve at a point 50 mm from the focus. A B 1. Draw a vertical line AB of any length as directrix and mark a point C on it. C 2. Draw a horizontal line CD of any length from point C as axis D 3 Prove that the lines AB', BA', and the perpendicular from 0 on the hypothenuse meet in a point. 11. Let P be any point (a, a) of the line x - y = 0, other than the origin. Through P draw two lines, of arbitrary slopes XI and X2, intersecting the x-axis in A1 and A2 and the y-axis in B1 and B2 respectively

C e where R and C c are the radius, and the point of intersection between the cylinder's axis and the plane, respectively, C e = x e, y e, z 0 T, a e and b e are the center, semi-major length and semi-minor length of the ellipse in the coordinate system of the intersecting plane, respectively, Rot is the rotation matrix that takes the plane.