Find the eccentricity of an ellipse with foci (+9, 0) and vertices (+10, 0).

Answer 1

Step 1:

The foci of the ellipse is .

The vertices of the ellipse are .

Observe the foci and vertices.

y -coordinate are equal and lie on the x-axis, so the ellipse is horizontal and center is at origin.

Ellipse equation :

The standard form of the horizontal ellipse is .

Where a is the length of the semi major axis, b is the length of the semi minor axis.

Here center of the ellipse is .

Foci of the ellipse is .

Vertices of the ellipse are .

The distance between center and vertex is a.

The distance between center and focus is c.

Eccentricity is .

Step 2:

The foci of the ellipse is .

The vertices of the ellipse are .

The distance between center and focus is .

The distance between center and vertex is .

Substitute and in eccentricity.

Therefore the eccentricity is .

Solution :

Eccentricity is .