Question

Given the foci of (8,0) and the difference of the focal radii = 6, find the equation of the hyperbola

Answer 1

Given :

The foci of hyperbola are (8,0) and (-8,0) .

The difference of the focal radii = 6.

To Find :

The equation of the hyperbola.

Solution :

We know, distance between foci is given by :

2c = 8 - (-8)

c = 8

Also, difference between the foci or focal distance is given by :

2a = 6

a = 3

Now, we know for hyperbola :

$b^2 +a^2 = c^2\\\\b^2={c^2-a^2}\\\\b^2 = 64-9\\\\b^2 = 55$

General equation of hyperbola is :

$\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1\\\\\dfrac{x^2}{9}+ \dfrac{y^2}{55}=1$

Hence, this is the required solution.