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Question

If the vertices of a hyperbola be at (2,0) and (2,0) and one of its foci be at (3,0), then which of the following is/are correct?


A
eccentricity of the hyperbola is 32
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B
(6,52) does not lie on hyperbola
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C
length of the latus rectum is 5 unit
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D
(26,5) does not lie on hyperbola
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Solution

The correct options are
A eccentricity of the hyperbola is 32
B (6,52) does not lie on hyperbola
C length of the latus rectum is 5 unit
Let hyperbola be
x2a2y2b2=1
Given a=2,ae=3e=32
As, (ae)2=a2+b2
9=4+b2
b2=5
Equation of Hyperbola is
x24y25=1
Length of the latus rectum
=2b2a=5 unit
On substituting the coordinates of the points given in options, we can say that only the point (6,52) does not satisfy the equation of hyperbola.

Mathematics

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