Question

Find an equation for the conic that satisfies the given conditions.

Ellipse,     foci (±2, 0),    Vertices  (±5, 0)

Answer 1

Step 1:

Foci of the ellipse and vertices are .

The coordinate in foci and vertices are same, so the ellipse is horizontal.

Standard form of horizontal ellipse .

Where

is length of semi major axis and is length of semi minor axis.

Center is , vertices

Foci and .

Step 2:

Vertices

The coordinate of center is 0.

Add the equations (1) and (2).

Center .

Step 3:

Find the values of , .

Substitute in equation (1).

Foci .

Substitute in equation (3).

is the distance from center to each focus.

Comments

Contd...

Step 4:

Substitute , and in standard form.

.

Solution:

The ellipse equation is .