# How do you write an equation of an ellipse in standard form with foci (8, 0) and (-8, 0) if the minor axis has y-intercepts of 2 and -2?

##### 1 Answer

Use x- and y-intercepts to deduce standard form ellipse coefficients. Deduce x-intercepts from distance from the foci to known points.

#### Explanation:

We can see from the symmetry of the given points that this ellipse is centred at

When

A definition of an ellipse is the set of points the sum of whose distances from the two foci is a constant. We can from the given information deduce that distance sum - the distance from both foci to either y-intercept is

Let the positive x-intercept be at

Thus