Book edition OER 2017

Author(s) OPENSTAX

Pages 1346 pages

ISBN 9780998625720

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Short Answer

In the following exercises, graph each ellipse.
$\frac{x^{2}}{16} + \frac{y^{2}}{36} = 1 .$

The graph of the ellipse is

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information

The equation of the ellipse is $\frac{x^{2}}{16} + \frac{y^{2}}{36} = 1 .$

Step 2. Concept used

The standard form of the ellipse with

$Centre: (0, 0) is$

\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1 a > b \Rightarrow major axis is x - axis with end points (- a, 0),(a,0) b > a \Rightarrow major axis is y - axis. with end points ((0, - b),(0,b)

Step 3. Find the center and major axis

$\frac{x^{2}}{16} + \frac{y^{2}}{36} = 1$

Compare with the standard form of the ellipse

localid="1645432640134" $Center (0, 0), 36 > 16 and a^{2} = 16 \Rightarrow a = \pm 4 b^{2} = 36 \Rightarrow b = \pm 6$

Major axis:

Onlocalid="1645425899245" $y - axis$ with endpoints $(0, - 6), (0, 6) .$

Minor axis:

Onlocalid="1645426041274" $x - axis with endpoints (- 4, 0), (0, 4) .$

Step 4. Graph the ellipse

The graph of the ellipse is

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Intermediate Algebra

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Short Answer

In the following exercises, graph each ellipse.
$\frac{x^{2}}{16} + \frac{y^{2}}{36} = 1 .$

Step by Step Solution

Step 1. Given information

Step 2. Concept used

Step 3. Find the center and major axis

Step 4. Graph the ellipse

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Step by Step Solution

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In the following exercises, graph each ellipse.
$\frac{x^{2}}{16} + \frac{y^{2}}{36} = 1 .$