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 x²/a² - y²/b² = 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, c² = a² + b²

Hence,

⇒ a² + 12² = 13²

⇒ a² = 169 - 144

⇒ a² = 25

Thus, the equation of the hyperbola is y²/25 - x²/144 = 1

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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 y²/25 - x²/144 = 1 while the Foci are (0, ± 13), the conjugate axis is of length 24