Chapter 11: Q. 102 (page 1118)

In the following exercises, graph each ellipse.
$\frac{x^{2}}{16} + \frac{y^{2}}{36} = 1 .$

Short Answer

Expert verified

The graph of the ellipse is

Step by step solution

Step 1. Given information

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

Step 2. Concept used

The standard form of the ellipse with

$Centre: (0, 0) is$

\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)

Step 3. Find the center and major axis

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

Compare with the standard form of the ellipse

localid="1645432640134" $Center (0, 0), 36 > 16 and a^{2} = 16 \Rightarrow a = \pm 4 b^{2} = 36 \Rightarrow b = \pm 6$

Major axis:

Onlocalid="1645425899245" $y - axis$ with endpoints $(0, - 6), (0, 6) .$

Minor axis:

Onlocalid="1645426041274" $x - axiswithendpoints (- 4, 0), (0, 4) .$

Step 4. Graph the ellipse

The graph of the ellipse is

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In the following exercises, graph each ellipse.
$\frac{x^{2}}{16} + \frac{y^{2}}{36} = 1 .$

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.x216+y236=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

Discrete Mathematics

Decision Maths

Probability and Statistics

Mechanics Maths

Pure Maths

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Study anywhere. Anytime. Across all devices.

In the following exercises, graph each ellipse.
$\frac{x^{2}}{16} + \frac{y^{2}}{36} = 1 .$