Chapter 11: Q. 101 (page 1118)

In the following exercises, graph each ellipse.
$\frac{x^{2}}{25} + \frac{y^{2}}{36} = 1 .$

Short Answer

Expert verified

The graph of the ellipse is

Step by step solution

Step 1. Given information

The equation of the ellipse is $\frac{x^{2}}{25} + \frac{y^{2}}{36} = 1 .$

Step 2. Concept used

The standard form of the ellipse

with $Center: (0, 0) is$

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

Step 3. Find the center and major axis

Compare the given equation with the standard form of the ellipse

$\frac{x^{2}}{25} + \frac{y^{2}}{36} = 1 Center:(0,0), 36 > 25 and a^{2} = 25 \Rightarrow a = \pm 5 b^{2} = 36 \Rightarrow b = \pm 6$

Major axis:

On $y -$ axis with endpoints $(0, - 6), (0, 6) .$

Minor axis:

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

Step 4. Sketch the graph

The graph of the given equation is

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In the following exercises, graph each ellipse.
$\frac{x^{2}}{25} + \frac{y^{2}}{36} = 1 .$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Concept used

Step 3. Find the center and major axis

Step 4. Sketch the graph

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In the following exercises, graph each ellipse.x225+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. Sketch the graph

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Probability and Statistics

Theoretical and Mathematical Physics

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Study anywhere. Anytime. Across all devices.

In the following exercises, graph each ellipse.
$\frac{x^{2}}{25} + \frac{y^{2}}{36} = 1 .$