Question

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

Vertices: (±7, 0);   foci: (±2, 0)

Answer 1

Step 1:

The vertices and foci .

The center of the ellipse, .

The foci of the ellipse, .

The vertices of the ellipse is .

The major axis is parallel to -axis.

The standard form of the ellipse equation when the axis is horizontal, with vertex at origin is

.

Step 2:

One of the foci is .

Substitute in .

The distance from center to focus is is .
One of the vertex is .

Substitute in .

The distance from center to vertex is is .

Find b value, .

Substitute and in .

.

Step 3:

Substitute in standard form of the ellipse equation.

The ellipse equation is

Solution :

The ellipse equation is