1. Write an equation for an ellipse with foci (0, +4) and co-vertices (+ 2, 0).

Answer 1

Step 1:

The foci of the ellipse is .

The co-vertices of the ellipse is .

Observe the foci.

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

Ellipse equation :

The standard form of the vertical 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 .

Co-vertices of the ellipse are .

The distance between center and vertex is a.

The distance between center and focus is c.

The distance between center and co-vertex is b.

Condition is .

Step 2:

The foci of the ellipse is .

The co-vertices of the ellipse is .

The distance between center and focus is .

The distance between center and co-vertex is .

Substitute and in .

Therefore the vertices of the ellipse are .

Comments

Contd...

Substitute and in the standard form of vertical ellipse.

Therefore the equation of the ellipse is .

Solution :

The equation of the ellipse is .