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Question

Equation of the hyperbola with vertices at (±5,0) and foci at (±7,0) is

A
24x225y2=600
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B
25x224y2=600
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C
x225y224=1
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D
x224y225=1
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Solution

The correct options are
A 24x225y2=600
C x225y224=1
Vertices(±5,0)Foci(±7,0)
a=±5 and ae=±7
And e=75
We know e=1+b2a2
On squaring both sides we get:
e2=1+b2a2
Or 4925=1+b225
Or b225=2425
b2=24
The equation of hyperbola is
x225y224=1
24x225y2=600

Hence, Option [A] and [C] are correct.

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