Step 1:

The conic equation is

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

Center is , vertices

Foci and

Where

In this case

Vertices are

Foci

Eccentricity

Solution:

, vertices

Foci ,

Graph:

Draw the coordinate plane.

Plot the center, vertices and foci of ellipse.

Then sketch the ellipse, use the semi major axis length is 6 units and semi minor axis length is 3.46 units.