Hyperbola

Hyperbola P-V Diagram Hyperbola Directrix Focus Method

Defination of an Hyperbola : -

These are the loci of points moving in a plane such that the ratio of it’s distances from a fixed point and a fixed line always remains constant . The ratio is called eccentricity(E).For Hyperbola, it is E>1 .

Hyperbola P-V Diagram



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

Construction

Step 1. Take pressure on vertical axis and Volume on horizontal axis.

Step 2. Divide both the axes in ten equal parts. Name these parts from 1 to 10.

Step 3. Now according to the table given below locate the points on the graph.



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Hyperbola Directrix Focus Method


PROBLEM 2 : 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 AB and line F remains constant and equal to 2/3. Draw locus of point P. { Eccentricity = 2/3 }

Construction

Step 1. Draw a vertical line AB and point F 50 mm from it. Divide 50 mm distance in 5 parts.

Step 2. Name 2nd part from AB as V. It is 20mm and 30mm from AB and F line resp. It is first point giving ratio of it’s distances from AB and F 2/3 i.e 20/30.

Step 3. Form more points giving same ratio such as 30/45, 40/60, 50/75 etc. Taking 30,40 and 50 mm distances from line AB, draw three vertical lines to the right side of it.

Step 4. Now with 45, 60 and 75 mm distances in compass cut these lines above and below, with F as center.

Step 5. Join these points through V in smooth curve. This is required locus of P.It is the required hyperbola.

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