Problem 38RE

Eccentricity-directrix approach Find an equation of the following curves, assuming the center is at the origin. Graph the curve, labeling vertices, foci, asymptotes (if they exist), and directrices.

An ellipse with foci (±4, 0) and directrices x = ±8

Solution 38RE

Given an ellipse with foci (±4, 0) and directrices x = ±8

Step 1:

Find an equation of the following curves, assuming the center is at the origin

The general equation of a ellipse is

The general form of foci is and directrix is

Therefore and

Therefore

Therefore

We have the formula

Therefore

is the equation of the ellipse.