Find the equations of the hyperbola satisfying the given conditions Vertices (0, ± 5), foci (0, ± 8)

Asked by Pragya Singh | 1 year ago |  85

##### Solution :-

Vertices (0, ± 5) and foci (0, ± 8)

Here, the vertices are on the y-axis.

So, the equation of the hyperbola is of the form

$$\dfrac{x^2}{a^2}$$ +$$\dfrac{y^2}{b^2}$$ = 1

Since, the vertices are (0, ±5), so, a = 5

Since, the foci are (0, ±8), so, c = 8

It is know that, a2 + b2 = c2

So, 52 + b2 = 82

b2 = 64 – 25 = 39

The equation of the hyperbola is

$$\dfrac{y^2}{25}-\dfrac{x^2}{39}=1$$

Answered by Abhisek | 1 year ago

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