Question

Find the vertices and foci of the ellipse. Graph the given equation.

Answer 1

Step 1:

The ellipse equation is .

Rewrite the equation as

Compare with standard form of horizontal ellipse with center at origin .

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

Vertices , co-vertices and foci

Where .

In this case center , .

Vertices  .

Co-vertices .

is the distance from the center to each focus.

Foci .

Step 2:

Graph:

Draw the coordinate plane.

Plot the center, vertices, co-vertices and foci of the ellipse.

Then sketch the ellipse by using the semi major axis length is 5 units and semi minor axis length is 2 units.

Solution:

Vertices  and foci .

Graph of :

.