Find the equations of the hyperbola satisfying the given conditions Foci (0, ±13), the conjugate axis is of length 24.

Asked by Pragya Singh | 11 months ago |  111

1 Answer

Solution :-

Foci (0, ±13) and the conjugate axis is of length 24.

Here, the foci are on y-axis.

The equation of the hyperbola is of the form 

 \( \dfrac{x^2}{a^2}\) +\( \dfrac{y^2}{b^2}\) = 1

Since, the foci are (0, ±13), so, c = 13

Since, the length of the conjugate axis is 24,

2b = 24

b = \( \dfrac{24}{2}\)

= 12

It is known that, a2 + b2 = c2

a2 + 122 = 132

a2 = 169 – 144

= 25

The equation of the hyperbola is 

\( \dfrac{y^2}{25}- \dfrac{x^2}{144}=1\)

Answered by Abhisek | 11 months ago

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