Question

Q1) Determine the equation of the hyperbola which satisfies the given conditions: Foci (0, ±13), the conjugate axis is of length 24.




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Answer 1

$\huge\underline \mathfrak\orange{Answer}$

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

Here, the foci are onthe y - axis.

Therefore, the equation of the hyperbola is of the form $\frac{y²}{a²}$ - $\frac{x²}{b²}$ = 1

Since the foci are (0, ±13), c = 13.

Since the length of the conjugate axis is 24, 2b = 24

⇒ b = 12

We know that a²+ b² = c²

∴ a²+ 12² = 13²

⇒ a² = 169 – 144 = 25

Thus, the equation ofthe hyperbola is $\frac{y²}{25}$ - $\frac{x²}{144}$ = 1

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Answer 2

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