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.
Center at $(1, 2)$ : focus at $(1, 4)$ : contains the point $(2, 2)$

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

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1 . Given information.

Center at $(1, 2)$ : focus at $(1, 4)$ contains the point $(2, 2)$ .

Since the center and the focus lie on the line $x = 1$ , thus the major axis is parallel to the y-axis.

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

Since, the point $(2, 2)$ lies on the ellipse

$\frac{{(2 - 1)}^{2}}{b^{2}} + \frac{{(2 - 2)}^{2}}{a^{2}} = 1 b^{2} = 1$

Step 2. The equation of ellipse.

Substitute $c = 2$ and $a = 1$ we get.

$b^{2} = a^{2} - c^{2} a^{2} = b^{2} + c^{2} a^{2} = 1 + 4 a^{2} = 5$

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

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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.
Center at $(1, 2)$ : focus at $(1, 4)$ : contains the point $(2, 2)$

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. Center at (1,2): focus at (1,4): contains the point (2,2)

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.
Center at $(1, 2)$ : focus at $(1, 4)$ : contains the point $(2, 2)$