# How do you write the equation of a hyperbola given foci at (1, 5) and (7, 5) and with vertices at (2, 5) and (6, 5)?

##### 1 Answer

Sep 6, 2016

Use the equation of hyperbola and

#### Explanation:

The foci and the vertices all lie along the horizontal line y=5, so the hyperbola opens left/right. This implies that the x term goes first and the y term is subtracted.

The center is half way between the vertices at (4.5) = (h,k).

The vertices are 2 units from the center, so a=2.

The foci are 3 units from center, so c =3.

Using

Plugging into

gives