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 at (-2,0); veryices at (1,0) and (-1,0)

The equation is?

Solution

Foci (-2,0)     vertices(1,0) and (-1,0)

This is of the form

(x-h)²/a²-(y-k)²/b²=1

Here centre (h,k) is (0,0)

Vertices is given by (h+-a,k)

therefore a=1

Foci is given by (h+-c,k)

Therefore c=2

c²=a²+b²

4=1+b²

b²=3

Required hyperbola is

x²/1 - y²/3=1