Question

Use a graphing utility to graph the ellipse.Find  the  center,  foci,  and  vertices.(Recall  that  it  may  be necessary to solve the equation for y and obtain two equations.)

5x^2 + 3y^2 = 15

Answer 1

Step 1 :

The ellipse equation is .

Convert the equation into standard form of ellipse.

Compare it with standard form of ellipse .

Where, center as an origin, , and major axis is vertical,

Foci , .

Vertices .

is the length of the major axis and

is the length of the minor axis.

Step 2 :

Center is origin : .

.

Now .

Foci of the ellipse : .

Vertices of the ellipse : .

Step 3 :

Graph the ellipse.

Graph the equation .

Plot the center point .

Plot the focus points .

Plot the vertex points .

Plot the two points left and right to the center and .

Solution :

Center , foci , and vertices .

The graph of the ellipse is :