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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 11: Q. 114 (page 1118)

In the following exercises, find the equation of the ellipse shown in the graph.

Short Answer

Expert verified

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

Step by step solution

01

Step 1.Given information

The graph of the ellipse is

02

Step 2.Concept used

The standard form of the ellipse with a center at the origin is

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

03

Step 3.Find the equation of the ellipse

From the given graph center at the origin.

The major axis is on $y -$ axis with endpoints $(0, - 6), (0, 6) .$ So, $b = 6 \Rightarrow b^{2} = 36 .$

The minor axis is on $x -$ axis with endpoints

$(- 4, 0), (4, 0) .$ So,role="math" localid="1645530673898" $a = 4 \Rightarrow a^{2} = 16 .$

Hence, the equation of the ellipse is

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

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Most popular questions from this chapter

Simplify the rational expression $\frac{p^{3} + 3 p^{2} + 4 p + 12}{p^{2} + p - 6} .$

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