Question

Find the vertices and foci of the ellipse. Graph the given equation.

4y^2 + x^2 = 8

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 horizontal ellipse .

Where

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

Center is , vertices

Foci and .

In this case .

Center is .

Vertices

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 2.82 units and semi minor axis length is 1.414 units.

Solution:

Center , vertices .

Foci and .