# How do you find an equation of hyperbola with given foci and asymptote: Foci: (0,0) and (0,4) Asymptote: y= +/-[(1/2)]x + 2?

##### 1 Answer

Aug 9, 2017

The equation of the hyperbola is

#### Explanation:

The foci are

The center is

The equations of the asymptotes are

Therefore,

Squaring both sides

Therefore,

The equation of the hyperbola is

**Verification**

The general equation of the hyperbola is

The foci are

graph{((y-2)^2-(x^2)/4-1)(y-2-1/2x)(y-2+1/2x)=0 [-6.76, 7.28, -1.425, 5.6]}