Chapter 11: Q. 100 (page 1118)

In the following exercises, graph each ellipse.
$\frac{x^{2}}{9} + \frac{y^{2}}{25} = 1 .$

Short Answer

Expert verified

The graph of the ellipse is

Step by step solution

Step 1. Given information

The equation of the ellipse is $\frac{x^{2}}{9} + \frac{y^{2}}{25} = 1 .$

Step 2. Conceptused

The standard form of the ellipse with

Center $(0, 0)$ is

localid="1645528234928" $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1 a > b \Rightarrow majoraxisis x - axiswithendpoints (- a, 0),(a,0) b > a \Rightarrow majoraxisis y - axis.withendpoints ((0, - b),(0,b)$

Step 3. Find the center and major axis

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

Compare with the standard form of the ellipse

localid="1645434250033" $center (0,0) 25 > 9 and a^{2} = 9 \Rightarrow a = \pm 3 b^{2} = 25 \Rightarrow b = \pm 5$

Major axis:

On $y -$ axis with endpoints $(0, - 5), (0, 5) .$

Minor axis:

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

Step 4. Sketch the ellipse

The graph of the ellipse is shown below.

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In the following exercises, graph each ellipse.
$\frac{x^{2}}{9} + \frac{y^{2}}{25} = 1 .$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Conceptused

Step 3. Find the center and major axis

Step 4. Sketch the ellipse

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In the following exercises, graph each ellipse.x29+y225=1.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Conceptused

Step 3. Find the center and major axis

Step 4. Sketch the ellipse

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Calculus

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Probability and Statistics

Study anywhere. Anytime. Across all devices.

In the following exercises, graph each ellipse.
$\frac{x^{2}}{9} + \frac{y^{2}}{25} = 1 .$