# Find the equation of the hyperbola satisfying the given conditions: Foci (0, ± 13), the conjugate axis is of length 24

**Solution:**

Foci (0, ± 13),

the conjugate axis is of length 24.

Here, the foci are on the y-axis.

Therefore,

the equation of the hyperbola is of the form x^{2}/a^{2} - y^{2}/b^{2} = 1

Since the foci are (0, ± 13), c = 13

Since the length of the transverse axis is 24,

Then,

⇒ 2b = 24

⇒ b = 12

We know that, c^{2} = a^{2} + b^{2}

Hence,

⇒ a^{2} + 12^{2} = 13^{2}

⇒ a^{2} = 169 - 144

⇒ a^{2} = 25

Thus, the equation of the hyperbola is y^{2}/25 - x^{2}/144 = 1

NCERT Solutions Class 11 Maths Chapter 11 Exercise 11.4 Question 11

## Find the equation of the hyperbola satisfying the given conditions: Foci (0, ± 13), the conjugate axis is of length 24

**Summary:**

The equation of the hyperbola is y^{2}/25 - x^{2}/144 = 1 while the Foci are (0, ± 13), the conjugate axis is of length 24

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