   Chapter 12.2, Problem 40E ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

#### Solutions

Chapter
Section ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

# 39-56 Finding the Equation of an Ellipse Find an equation for the ellipse that satisfies the given conditions.40. Foci: ( 0 , ± 3 ) , vertices: ( 0 , ± 5 ) .

To determine

The equation for the ellipse for the given conditions.

Explanation

Given:

The foci and vertices of the ellipse is,

Foci: (0,±3)

Vertices: (0,±5)

Approach:

The basic equation for an ellipse which is used is as follows,

x2b2+y2a2=1

Where a and b are constant values.

Expression to find vertices is,

V=(0,±a)

Expression to find Foci is,

F=(0,±c),

Where, c2=a2b2

Calculation:

Compare the standard coordinates of vertices and the given coordinates of the vertices.

V=(0,±a)=(0,±5)

Thus,

a=5.

Compare the standard coordinates of foci and the given coordinates of the foci.

F=(0,±c)=(0,±3)

Thus,

c=3.

Also as,

c2=a2b2

Substitute 3 for c and 5 for a in the above relation to calculate the value of b

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started 