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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. 110 (page 1118)

In the following exercises, graph each ellipse.
$9 x^{2} + 25 y^{2} = 225$

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 $9 x^{2} + 25 y^{2} = 225$

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. Convert into standard form

$9 x^{2} + 25 y^{2} = 225 Given \frac{9 x^{2}}{225} + \frac{25 y^{2}}{225} = \frac{225}{225} Dividewith225onbothsides \frac{x^{2}}{25} + \frac{y^{2}}{9} = 1 Simplify$

04

Step 4.Find the center and major axis

$\frac{x^{2}}{25} + \frac{y^{2}}{9} = 1$

Compare the given equation with the standard form of the ellipse

$Center:(0,0), 25 > 9 and a^{2} = 25 鈬� a = 卤 5 b^{2} = 9 鈬� b = 卤 3$

Major axis:

On $x -$ axis with end points $(- 5, 0), (5, 0) .$

Minor axis

On $y -$ axis with endpoints $(0, - 3, (0, 3) .$

05

Step 5. Sketch the graph

The graph of the ellipse is

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Most popular questions from this chapter

In the following exercises, write with a rational exponent.

Part (a): $\sqrt[3]{25 a}$

Part (b): $\sqrt{3 b}$

Part (c): $\sqrt[8]{40 c}$

In the following exercises, multiply the rational expressions. $\frac{5 c^{2} + 9 c + 2}{c^{2} - 25} . \frac{c^{2} + 10 c + 25}{3 c^{2} - 14 c - 5}$

In the following exercises, solve.

$q^{3} + 3 q^{2} + 2 q = 0$

Simplify each expression:

$鈸� \frac{y^{43}}{y^{37}} 鈸� \frac{10^{15}}{10^{7}} 鈸� \frac{m^{7}}{m^{15}} 鈸� \frac{9^{8}}{9^{19}}$

In the following exercises, factor completely.

$8 x^{3} - 27 y^{3}$

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