Question

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This hyperbola is centered at the origin. Find its equation. Foci: (0,-9) and (0,9) Vertices: (0,-7) and (0,7)​

Answer 1

The equation of hyperbola :
`(y^(2) )/(49 ) - (x^(2) )/(32 )`

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

`(y^(2) )/(a^(2) ) - (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

`(y^(2) )/(49 ) - (x^(2) )/(32 )`