Question

Identify the conic as a circle or an ellipse.Then find the center, radius, vertices, foci, and eccentricity of the conic (if applicable), and sketch its graph.

Answer 1

Step 1:

The conic equation is .

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

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 .

Eccentricity .

Step 2:

Graph:

Draw the coordinate plane.

Plot the center, vertices and foci of ellipse.

Then sketch the ellipse by using the semi major axis length is 5 units and semi minor axis length is 4 units.

Solution:

Center , vertices .

Foci and .