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 $(1, 2)$ : vertex at $(4, 2)$ :contains the point $(1, 5)$

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

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1 . Given information.

Center at $(1, 2)$ : vertex at $(4, 2)$ :contains the point $(1, 5)$ .

On comparing with the standard equation of the ellipse $\frac{{(x - h)}^{2}}{a^{2}} + \frac{{(y - k)}^{2}}{b^{2}} = 1$

Here, $x = 1, y = 5, h = 1, k = 2$ and $h + a = 4 a = 4 - 1 a = 3$

Now put these values in the equation of the ellipse.

$\frac{{(1 - 1)}^{2}}{3^{2}} + \frac{{(5 - 2)}^{2}}{b^{2}} = 1 \frac{0}{9} + \frac{9}{b^{2}} = 1 \frac{9}{b^{2}} = 1 b^{2} = 9$

Step 2. The equation of ellipse.

Substitute the value of $a^{2} = 9$ and $b^{2} = 9$ we get

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

Step 3 .Graph of the ellipse .

The major axis is parallel to the x-axis.So the vertices are $a = 3$ units left and right of the center $(1, 2)$ .Therefore the vertices are localid="1646732539408" $v_{1} = (- 2, 2)$ and localid="1646732554304" $v_{2} = (4, 2)$

Since,

localid="1646732713719" $c^{2} = a^{2} - b^{2} c^{2} = 9 - 9 c^{2} = 0$

Major axis is parallel to the x-axis, foci are localid="1646732722940" $(1 - 0, 2)$ and localid="1646732737337" $(1, 2)$ .

We use the value localid="1646732752572" $b = 3$ to find the two points above and below the center as localid="1646732764537" $(1, - 1)$ and localid="1646732779266" $(1, 5)$

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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 $(1, 2)$ : vertex at $(4, 2)$ :contains the point $(1, 5)$

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): vertex at (4,2):contains the point(1,5)

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 $(1, 2)$ : vertex at $(4, 2)$ :contains the point $(1, 5)$