Question

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

Center:  (0, 4);  a = 2c;   Vertices: (- 4, 4), (4, 4)

Answer 1

Step 1:

 Center of the ellipse is and .

Vertices of the ellipse  are .

and .

Substitute center point values in above point.

.

Major axis length .

Eccentricity .

Step 2:

For an ellipse .

.

Standard form of the ellipse is

Substitute center and values in above standard form.

.

Solution:

Standard form of the ellipse is .