   Chapter 12.4, Problem 31E ### 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

# SKILLS 29-34 ■ Finding the Equation of a Shifted Conic Find an equation for the conic whose graph is shown. To determine

To find:

The equation of the conic.

Explanation

Given:

The graph of the conic section is given below.

Figure (1)

Approach:

For an equation in x and y, if the value of x is replaced by x±h, then the graph is shifted horizontally and if the value of y is replaced by y±k, then the graph is shifted vertically.

The equation of an ellipse centred at (h,k) is given by the following formula.

(xh)2a2+(yk)2b2=1...(1)

Calculations:

Consider the graph of the conic.

The coordinates of the major axis are (0,0) and (10,0).

The center of the ellipse is the midpoint of the major axis.

Therefore, the center of the ellipse is given below.

(10+02,0+02)=(5,0)

The length of the major axis is given by,

100=10

Therefore, the value a is given below.

a=102=5

The two foci of the ellipse are at (8,0) and (2.0).

The distance between the two foci is given below.

82=6

Therefore, the value of c is given below

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