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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 11: Q. 111 (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 $\frac{x^{2}}{9} + \frac{y^{2}}{25} = 1 .$

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 $(0, - 5), (0, 5)$ . So, $b = 5 \Rightarrow b^{2} = 25 .$

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

$(- 3, 0), (3, 0) .$ So, $a = 3 \Rightarrow a^{2} = 9 .$

Hence, the equation of the ellipse is

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

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Most popular questions from this chapter

Simplify the rational expression $\frac{x^{2} + 4 x - 5}{x^{2} - 2 x + 1}$

The number of hours it takes for ice to melt varies inversely with the air temperature. Suppose a block of ice melts in 2 hours when the temperature is 65 degrees Celsius.

Write the equation of variation.
How many hours would it take for the same block of ice to melt if the temperature was 78 degrees?

Simplify a Complex Rational Expression by Using the LCD.

In the following exercises, simplify each complex rational expression by using the LCD. $\frac{\frac{3}{s + 6} + \frac{5}{s - 6}}{\frac{1}{s^{2} - 36} + \frac{4}{s + 6}}$

Factor completely: $27 y^{2} - 48$

In the following exercises, add or subtract.

$\sqrt{- 75} + \sqrt{- 48}$

See all solutions

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