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.
Vertices at $(2, 5)$ and $(2, - 1)$ :c=2

The equation of the ellipse is $\frac{{(x - 2)}^{2}}{5} + \frac{{(y - 2)}^{2}}{9} = 1$ and graph of the ellipse is

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information.

Vertices at $(2, 5)$ and $(2, - 1)$ : $c = 2$

The vertices lies on the line $x = 2$ , thus the major axis is parallel to the y-axis.

The center is at the mid point of the vertices $(2, 2)$ .

The distance of the center from one of the foci is $c = 2$ .

The distance of the center from one of the vertices is $a = 3$ .

Step 2. The equation of ellipse.

Substitute $a = 3$ and $c = 2$ in $b^{2} = a^{2} - c^{2}$ we get.

$b^{2} = a^{2} - c^{2} b^{2} = 9 - 4 b^{2} = 5$

Substituting the values of $a^{2}$ and $b^{2}$ in the equation of the ellipse we get.

$\frac{{(x - 2)}^{2}}{5} + \frac{{(y - 2)}^{2}}{9} = 1$

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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.
Vertices at $(2, 5)$ and $(2, - 1)$ :c=2

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. Vertices at (2,5) and (2,-1):c=2

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.
Vertices at $(2, 5)$ and $(2, - 1)$ :c=2