Question

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Answer 1

Answer:

The equation of hyperbola :  $\frac{y^{2} }{49 } - \frac{x^{2} }{32 }$

Step-by-step explanation:

Given - This hyperbola is centered at the origin.

Foci: (0,-9) and (0,9) Vertices: (0,-7) and (0,7)​

To find - Find its equation.

Solution -

We know  that,

Equation of Hyperbola is represented by

$\frac{y^{2} }{a^{2} } - \frac{x^{2} }{b^{2} }$

Now,

Given that,

Foci : F(0, -9) and F'(0, 9)

So,

c = 9

And

Vertices : A(0,-7) and A'(0,7)​

So,

a = 7

Also, we know that,

c² = a² + b²

⇒b² = c² - a²

⇒b² = 9² - 7²

⇒b² = 81 - 49

⇒b² = 32

So,

The equation of hyperbola becomes

$\frac{y^{2} }{49 } - \frac{x^{2} }{32 }$