Find the equations of the hyperbola satisfying the given conditions Foci (±5, 0), the transverse axis is of length 8.

Asked by Pragya Singh | 1 year ago |  113

##### Solution :-

Foci (±5, 0) and the transverse axis is of length 8.

Here, the foci are on x-axis.

The equation of the hyperbola is of the form

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

Since, the foci are (±5, 0), so, c = 5

Since, the length of the transverse axis is 8,

2a = 8

a = $$\dfrac{8}{2}$$

= 4

It is known that, a2 + b2 = c2

42 + b2 = 52

b2 = 25 – 16

= 9

The equation of the hyperbola is

$$\dfrac{x^2}{16}- \dfrac{y^2}{9}=1$$

Answered by Abhisek | 1 year ago

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