Chapter 11: Q. 110 (page 1118)

In the following exercises, graph each ellipse.
$9 x^{2} + 25 y^{2} = 225$

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 $9 x^{2} + 25 y^{2} = 225$

Step 2. Concept used

The standard form of the ellipse

with Center at the origin 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. Convert into standard form

$9 x^{2} + 25 y^{2} = 225 Given \frac{9 x^{2}}{225} + \frac{25 y^{2}}{225} = \frac{225}{225} Dividewith225onbothsides \frac{x^{2}}{25} + \frac{y^{2}}{9} = 1 Simplify$

Step 4.Find the center and major axis

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

Compare the given equation with the standard form of the ellipse

$Center:(0,0), 25 > 9 and a^{2} = 25 \Rightarrow a = \pm 5 b^{2} = 9 \Rightarrow b = \pm 3$

Major axis:

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

Minor axis

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

Step 5. Sketch the graph

The graph of the ellipse is

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In the following exercises, graph each ellipse.
$9 x^{2} + 25 y^{2} = 225$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Concept used

Step 3. Convert into standard form

Step 4.Find the center and major axis

Step 5. Sketch the graph

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In the following exercises, graph each ellipse.9x2+25y2=225

Short Answer

Step by step solution

Step 1. Given information

Step 2. Concept used

Step 3. Convert into standard form

Step 4.Find the center and major axis

Step 5. Sketch the graph

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Mechanics Maths

Calculus

Theoretical and Mathematical Physics

Probability and Statistics

Statistics

Study anywhere. Anytime. Across all devices.

In the following exercises, graph each ellipse.
$9 x^{2} + 25 y^{2} = 225$