Question

Find the standard form of the equation of the ellipse with the given characteristics.

Foci: (0, 0), (0, 8);  major axis of length 16

Answer 1

Step 1:

The foci are  .

Let the points .

The standard form of the equation of ellipse with major axis is vertical,

.

Where a is the major axis and b is the minor axis.

The length of the major axis is .

The center of the ellipse is the average of the two points.

The center of the ellipse is .

Step 2:

The distance from center to one of the foci is .

The foci is lie on the major axis, units from the center is,

Substitute , and in .

The equation of the ellipse is

Solution :

The equation of the ellipse is