Chapter 11: Q. 107 (page 1118)

In the following exercises, graph each ellipse.
$4 x^{2} + 25 y^{2} = 100$

Short Answer

Expert verified

The graph of the ellipse is

Step by step solution

Step 1.Given information

The equation of the ellipse is $4 x^{2} + 25 y^{2} = 100$

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

$4 x^{2} + 25 y^{2} = 100 Given \frac{4 x^{2}}{100} + \frac{25 y^{2}}{100} = \frac{100}{100} Dividewith 100 onbothsides \frac{x^{2}}{25} + \frac{y^{2}}{4} = 1 Simplify$

Step 4. Find the center and major axis

Compare the given equation with the standard form of the ellipse

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

Center is $(0, 0)$

$25 > 4$

$a^{2} = 25 \Rightarrow a = \pm 5 b^{2} = 4 \Rightarrow b = \pm 2$

The major axis is on $x -$ axis with endpoints $(- 5, 0), (5, 0) .$

The minor axis is on $y -$ axis with endpoints $(0, - 2), (0, 2) .$

Step 5. Sketch the graph

The graph of the ellipse is

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

In the following exercises, graph each ellipse.
$4 x^{2} + 25 y^{2} = 100$

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

Applied Mathematics

Mechanics Maths

Calculus

Probability and Statistics

Geometry

Logic and Functions

Study anywhere. Anytime. Across all devices.

In the following exercises, graph each ellipse.4x2+25y2=100

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

Applied Mathematics

Mechanics Maths

Calculus

Probability and Statistics

Geometry

Logic and Functions

Study anywhere. Anytime. Across all devices.

In the following exercises, graph each ellipse.
$4 x^{2} + 25 y^{2} = 100$