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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 11: Q. 108 (page 1069)

In the following exercises, graph each ellipse.
$16 x^{2} + 9 y^{2} = 144$

Short Answer

Expert verified

The Graph of the given ellipse is given by

Step by step solution

01

Step 1.Given information

The equation of the ellipse is $16 x^{2} + 9 y^{2} = 144$

02

Step 2. Concept used

The standard form of the ellipse with Center at the origin is

$\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1 a > b 鈬� majoraxisis x - axiswithendpoints (- a, 0),(a,0) b > a 鈬� majoraxisis y - axis.withendpoints ((0, - b),(0,b)$

03

Step 3.Find the center and major axis

$16 x^{2} + 9 y^{2} = 144 Given \frac{16 x^{2}}{144} + \frac{9 y^{2}}{144} = \frac{144}{144} Dividewith 144 onbothsides \frac{x^{2}}{9} + \frac{y^{2}}{16} = 1 Simplify$

Compare the given equation with the standard form of the ellipse

$Center:(0,0), 16 > 9 and a^{2} = 9 鈬� a = 卤 3 b^{2} = 16 鈬� b = 卤 4$

Major axis:

on y-axis with end oints $(0, - 4), (0, 4) .$

Minor axis:

on role="math" localid="1645448767451" $x -$ axis with endpoints $(- 3, 0), (3, 0) .$

04

Step 4. Sketch the graph

The graph of the ellipse is shown below

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Most popular questions from this chapter

Factor completely, $5 x^{3} + 15 x^{2} - 20 x$

Show two different algebraic methods to simplify $4^{\frac{3}{2}}$ . Explain all your steps.

Use the Quotient Property to Simplify Radical Expressions

In the following exercises, use the Quotient Property to simplify square roots.

$a . \sqrt{\frac{72}{98}} b . \sqrt[3]{\frac{24}{81}} c . \sqrt[4]{\frac{6}{96}}$

Solve: ${(9 x + 9)}^{\frac{1}{4}} - 2 = 1$

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(a) $36^{\frac{1}{2}}$

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