Chapter 11: Q. 99 (page 1118)

In the following exercises, graph each ellipse.
$\frac{x^{2}}{4} + \frac{y^{2}}{25} = 1 .$

Short Answer

Expert verified

The Graph of the given ellipse is given by

Step by step solution

Step 1. Given information

The equation of the ellipse is

$\frac{x^{2}}{4} + \frac{y^{2}}{25} = 1$ .

Step 2. Concept used

The standard form of the ellipse with

center $(0, 0)$ is

localid="1645422226494" $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$

$a > b \Rightarrow$ major axis on $x -$ axis with x-intercepts $(- a, 0), (a, 0) .$
$b > a \Rightarrow$ major axis on $y -$ axis with $y -$ intercepts $(0, - b), (0, b) .$

Step 3. Find the center and major axis

$\frac{x^{2}}{4} + \frac{y^{2}}{25} = 1$

Compare with the standard form of the ellipse

Center $(0, 0) .$

Here, $9 > 4$

$a^{2} = 4 \Rightarrow a = \pm 2 b^{2} = 9 \Rightarrow b = \pm 3$

So,

$y -$ axis is the major axis with endpoints localid="1645424530502" $(0, - 3),(0,3).$

and

$x -$ axis is the minor axis with endpoints $(- 2, 0), (2, 0) .$

Step 4. Graph the ellipse

The graph of the ellipse is shown below.

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In the following exercises, graph each ellipse.
$\frac{x^{2}}{4} + \frac{y^{2}}{25} = 1 .$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Concept used

Step 3. Find the center and major axis

Step 4. Graph the ellipse

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In the following exercises, graph each ellipse.x24+y225=1.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Concept used

Step 3. Find the center and major axis

Step 4. Graph the ellipse

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Logic and Functions

Probability and Statistics

Theoretical and Mathematical Physics

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Study anywhere. Anytime. Across all devices.

In the following exercises, graph each ellipse.
$\frac{x^{2}}{4} + \frac{y^{2}}{25} = 1 .$