Question

In each of the following find the equations of the hyperbola satisfying the given conditions foci (0, ±13), conjugate axis = 24

Answer 1

Given: foci (0, ±13) and the conjugate axis is 24 

To find: equation of the hyperbola 

Formula used: 

The standard form of the equation of the hyperbola is,

\(\frac{x^2}{a^2} - \frac{y^2}{b^2} = -1\)

Length of the conjugate axis is 2b 

Coordinates of the foci for a standard hyperbola is given by (0, ±be)

According to question: 

2b = 24 and be = 13 

2b = 24

\(\Rightarrow\) b = \(\frac{24}{2}\)

⇒ b = 12 

⇒ b² = 144

be = 12

\(\Rightarrow\) 12 \(\times \)e = 13

\(\Rightarrow\) e = \(\frac{13}{12}\)

We know, 

a² = b²(e² – 1)

⇒ b² = 25

Hence, the equation of the hyperbola is: