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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 11: Q 11.44. (page 1110)

Find the equation of the ellipse shown.

Short Answer

Expert verified

The equation of an ellipse is $\frac{x^{2}}{9} + \frac{y^{2}}{4} = 1$ .

Step by step solution

01

Step 1. Given information

The graph of an ellipse is shown below:

02

Step 2. Determine whether the major axis is horizontal or vertical.

From the given figure, observe that the figure is an ellipse centered at the origin.

So, the equation of an ellipse is $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1 \dots (1)$ .

From the figure, observe that the major axis of an ellipse is horizontal.

03

Step 3. Find the value of a2 and b2.

The distance from the center to the vertex is $3$ .

So, $a = 3$ which implies $a^{2} = 9$ .

The minor axis is vertical and the distance from the center to the ellipse is $2$ .

So, $b = 2$ which implies $b^{2} = 4$ .

04

Step 4. Find the equation of an ellipse.

Substitute the values of $a^{2}$ and $b^{2}$ into the equation $(1)$ .

Thus, the equation of an ellipse is as follows:

$\frac{x^{2}}{9} + \frac{y^{2}}{4} = 1$

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Most popular questions from this chapter

Simplify $\sqrt{48}$ .

Use the Quotient Property to Simplify Radical Expressions

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

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

Simplify each expression:

$ⓐ \frac{y^{43}}{y^{37}} ⓑ \frac{10^{15}}{10^{7}} ⓒ \frac{m^{7}}{m^{15}} ⓓ \frac{9^{8}}{9^{19}}$

Use the Quotient Property to simplify square roots.

$\sqrt{\frac{180 s^{10}}{144}}$

In the following exercises, factor each trinomial of the form

$x^{2} + b x + c x^{2} - 12 - 11 x$

See all solutions

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