Find the Center,foci,vertices, and eccentricity of the ellipse, and sketch its graph.

Question

Find the <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Center,foci,vertices, and eccentricity of the ellipse, and sketch its graph.

Answer 1

Step 1:

The ellipse equation is .

Convert the equation into standard form of ellipse by using completing square method.

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 with 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

Vertices

Co-vertices

Focus

Eccentricity .

Graph:

Draw the coodinate plane.

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

Then sketch the ellipse by using the semi major axis length is 3 units and semi minor axis length is 2 units.

Solution:

Center

Vertices

Focus

Eccentricity .

Graph of ellipse:

.