Question

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin.

Foci: (±5, 0); major axis of length 14

Answer 1

Step 1:

The foci of ellipse are .

The y -coordinate of foci is constant, so the ellipse is horizontal.

The standard form of a horizontal ellipse is .

Where (h, k ) is the center of ellipse.

a is the length semi major axis and b is the length semi minor axis.

The length of major axis is .

The center is the midpoint of foci .

center is .

Step 2:

The distance from the center to one of the foci is .

The distance between and is,

For ellipse .

Substitute and in .

Substitute , and in above standard form.

Solution :

The ellipse equation is .