   Chapter 12.CR, Problem 67E ### 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

# Families of Ellipses(a) Draw graphs of the following family of ellipses for k   =   1 , 2 , 4 ,   and   8 . x 2 16 + k 2 + y 2 k 2 = 1 (b) Prove that all the ellipses in part (a) have the same foci.

To determine

(a)

To draw:

The graph of the following family of ellipses for k=1, 2, 4, and 8.

x216+k2+y2k2=1

Explanation

Approach:

Write the expression of y for the value of k in graphing calculator. Then put the expression one by one in the graphing calculator for plotting the curves.

Calculation:

For k=1, the equation of ellipse is,

x217+y21=1

y=±1x217

For k=2, the equation of ellipse is,

x220+y24=1

y=±21x220

For k=4, the equation of ellipse is,

x232+y216=1

y=±41x232

For k=8, the equation of ellipse is,

x280+

To determine

(b)

To prove:

All the ellipses in part (a) have the same foci.

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