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  • If the vertex of a hyperbola bisects the distance between its centre and the corresponding focus, then the ratio of the square of its conjugate axis to the square of its transverse axis is<div

If the vertex of a hyperbola bisects the distance between its centre and the corresponding focus, then the ratio of the square of its conjugate axis to the square of its transverse axis is

Option: 1

3


Option: 2

1


Option: 3

0


Option: 4

-2


Answers (1)

best_answer

Let the hyperbola be\mathrm{\frac{x^2}{a^2}-\frac{y^2}{b^2}=1} Then \mathrm{ 2 a=a c,}i.e.\mathrm{ e=2} Therefore,

\mathrm{ \frac{b^2}{a^2}=e^2-1=3 \quad \text { or } \quad \frac{(2 b)^2}{(2 a)^2}=3}

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