Book edition 6th

Author(s) Sullivan

Pages 1200 pages

ISBN 9780321795465

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Short Answer

Find an equation for each ellipse. Graph the equation by hand.
Foci at $(5, 1)$ and $(- 1, 1)$ : length of the major axis is $8$ .

The equation of the ellipse is $\frac{{(x - 2)}^{2}}{16} + \frac{{(y - 1)}^{2}}{7} = 1$ and graph of the ellipse is

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information.

Foci at $(5, 1)$ and $(- 1, 1)$ :length of the major axis is $8$ .

The foci lie on the line $y = 1$ , so the major axis is parallel to the x-axis.

The two foci $(5, 1)$ and $(- 1, 1)$ , we can find the center of the ellipse which is the midpoint of these two points.

Thus, the center of the ellipse is $(2, 1)$ .

Step 2. The equation of ellipse.

The length of the major axis $2 a$ is given as $8$ . So, we have

$2 a = 8 a = 4$

The distance from the center of the ellipse $(2, 1)$ to the focus $(5, 1)$ is $c = 3$

Substitute $c = 3$ and $a = 4$ in

role="math" localid="1646719438001" $b^{2} = a^{2} - c^{2} b^{2} = 4^{2} - 3^{2} b^{2} = 16 - 9 b^{2} = 7$

The equation of ellipse is $\frac{{(x - 2)}^{2}}{16} + \frac{{(y - 1)}^{2}}{7} = 1$

Step 3 .Graph of the ellipse

The major axis parallel to the x- axis. So the vertices of the ellipse are $a = 4$ units left and right of the center $(2, 1)$ .

Thus, the vertices are $v_{1} = (- 2, 1)$ and $v_{2} = (6, 1)$ .

We use $b = \sqrt{7}$ to find the two points above and below the center. The two points are $(2, 1 + \sqrt{7})$ and $(2, 1 - \sqrt{7})$ .

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Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

Find an equation for each ellipse. Graph the equation by hand.
Foci at $(5, 1)$ and $(- 1, 1)$ : length of the major axis is $8$ .

Step by Step Solution

Step 1. Given information.

Step 2. The equation of ellipse.

Step 3 .Graph of the ellipse

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Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

Find an equation for each ellipse. Graph the equation by hand. Foci at (5,1) and (-1,1): length of the major axis is 8.

Step by Step Solution

Step 1. Given information.

Step 2. The equation of ellipse.

Step 3 .Graph of the ellipse

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Find an equation for each ellipse. Graph the equation by hand.
Foci at $(5, 1)$ and $(- 1, 1)$ : length of the major axis is $8$ .