Find the standard form of the equation of the hyperbola sati

Find the standard form of the equation of the hyperbola satisfying the given conditions:

Foci (-5,0),(5,0) ; vertices (-3,0), (3,0)

Solution

This hyperbola is of the form

(x-h)²/a² - (y-k)²/b²=1

In the given question centre(h,k) = (0,0)

Where vertices= (h+-a,k)

And according to the question

h+a=3

a=3

focii=(h+-c,k)

And according to question

h+c= 5

c=5

c²=a²+b²

25= 9 + b²

b=4

required equation is

x²/9 - y²/16=1