Problems On Hyperbola

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Problems On Hyperbola


HYPERBOLA BY  A POINT OF KNOWN CO-ORDINATES, P-V DIAGRAM, AND BY DIRECTRIX FOCUS METHOD.

HYPERBOLA BY A POINT OF KNOWN CO-ORDINATES...

1. Point P is 40 mm and 30 mm from horizontal and vertical axes respectively. Draw Hyperbola through it.

SOLUTION STEPS:

  1. Extend the horizontal line from P to the 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.Let them cut part [P-B] also at 1,2,3,4 points.

  5. From horizontal 1,2,3,4 draw vertical lines downwards

  6. From vertical 1,2,3,4 points [from P-B] draw horizontal lines.

  7. Line from 1 horizontal and line from 1 vertical will meet at P1. Similarly mark P2, P3, P4 points.

  8. Repeat the procedure by marking four points on an upward vertical line from P and joining all those tp pole O. Name these points P6, P7, P8, etc, and join them by a smooth curve.


hyperbola by a point of know co-ordinates problem no 1
HYPERBOLA BY P-V DIAGRAM...

2. A sample of gas is expanded in a cylinder from 10 unit pressure to 1 unit pressure. Expansion follows law PV = Constant. If the initial volume being 1 unit, draw the curve of expansion. Also Name the curve.

From a table giving a few more values of P & V.
V    ×  C    =  P
10  × 1     = 10
5    ×  2    = 10
4    × 2.5  = 10
2.5 × 4     = 10
2    × 5     = 10
1    × 10   = 10


Now Draw a graph of pressure against volume. It is a PV diagram and it is Hyperbola. Take pressure on the vertical axis and Volume on the Horizontal axis.

hyperbola by p-v diagram problem no 2 HYPERBOLA BY DIRECTRIX FOCUS METHOD...

3. 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}SOLUTION STEPS:

  • Draw a vertical line AB  and point F 50 mm from it.

  • Divide 50 mm distance in 5 parts.

  • Name 2 part from F as V. It is 20 mm and 30 mm from F and AB line reps. It is the first point giving a ratio of its distance from F and AB 2/3 i.e. 20/30.

  • From more points giving the same ratio such as 30/45, 40/60, 50/75, etc.

  • Taking 45,60, and 75 distance from line AB, Draw three vertical lines to the right side of it.

  • Now with 30, 40, and 50 mm distances in compass cut these lines above and below with F as the center.

  • Join this point through V in a smooth curve.


This is a required locus of P. It is an ELLIPSE.hyperbola by diractrix focus method problem no 3 Please write comments if you find anything incorrect and if you have any queries about this topic or you want to share more information about the topic discussed above.