Problem 29E

Graphing ellipses Sketch the graph of the following ellipses. Plot and label the coordinates of the vertices and foci, and find the lengths of the major and minor axes. Use a graphing utility to check your work.

Solution 29E

Step 1:

In this problem we need to Plot and label the coordinates of the vertices and foci of the ellipse and we have to find the lengths of the major and minor axes.

The standard equation of the ellipse with center (0,0) and major axis on the y-axis is where a>b

Here we have

- Vertices of the ellipse:

Therefore the coordinates of the ellipse is

- Foci of the ellipse: where

Therefore the foci of the ellipse is