Step 1:

The conic equation is

The coefficients of and are the same sign but unequal coefficients. So the equation is ellipse.

Rewrite the equation as

Convert the equation in standard form of ellipse.

Compare it to standard form of vertical ellipse is .

Where

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

Center is , vertices

Foci and .

Where .

In this case .

Center is

Vertices are

Foci

Step 2:

Graph:

Draw the coordinate plane.

Plot the center, vertices and foci of ellipse.

Then sketch the ellipse, use the semi major axis length is 5 units and semi minor axis length is 4 units.

Solution:

Center , vertices .

Foci and ,.

.