# How do you write an equation of a ellipse with center (0,4) and a=2c, vertices (-4,4), (4,4)?

##### 1 Answer

#### Explanation:

The general form for an ellipse is either of the following:

In either case, the quantity

By convention of writing for all ellipses, the value

Although we do not know whether this is a horizontal or vertical ellipse, we can use this relationship to determine another fact:

We know from looking at the vertices of (-4, 4) and (4,4) provided, and the center of (0, 4), that the horizontal semi-axis length is 4. This is either the semi-major axis (if the ellipse is horizontally aligned), or the semi-minor axis.

At this point, we can choose which kind of ellipse we want to find. I will assume this is a horizontal ellipse and omit a solution for a vertical ellipse. If this is a horizontal ellipse, than the

Putting all of this together, and using the horizontal ellipse equation, gives us:

Graph:

graph{x^2/16 + (y-4)^2/12 = 1 [-6, 6, -2, 8]}