The conic equation is .

Since the coefficients of and are the same sign but unequal coefficients,

the equation represents an ellipse.

To change the expressions and into a perfect square trinomial,

add (half the x coefficient)² and add (half the y coefficient)² to each side

of the equation.

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 ,

Eccentricity .

Where .

In this case

Vertices are .

Now ,

Foci .

Eccentricity .

.

Graph:

Draw the coordinate plane.

Plot the center, vertices and foci of ellipse.

Then draw the ellipse, use the semi major axis length is 6 units and semi minor

axis length is 3.46 units.

Center , vertices , foci , and eccentricity

Graph the .