Chapter 11: Q. 105 (page 1118)

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

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

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

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.Find the center and major axis

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

Compare the given equation with the standard form of the ellipse

$Center:(0,0), 4 > 1 and a^{2} = 1 \Rightarrow a = \pm 1 b^{2} = 4 \Rightarrow b = \pm 2$

Major axis:

On $x -$ axis with endpoints $(- 1, 0), (1, 0) .$

Minor axis

On $y -$ axis with endpoints $(0, 2), (0, - 2)$

Step 4. Sketch the graph

The graph of the ellipse is shown below

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

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.x2+y24=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

Statistics

Mechanics Maths

Logic and Functions

Geometry

Discrete Mathematics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

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