Chapter 11: Q 11.39. (page 1108)

Graph: $\frac{x^{2}}{4} + \frac{y^{2}}{16} = 1$ .

Short Answer

Expert verified

The graph of an ellipse is shown below:

Step by step solution

Given Information

The given ellipse is $\frac{x^{2}}{4} + \frac{y^{2}}{16} = 1$ .

Step 2. Write the equation in standard form.

The standard form of an ellipse is $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1 \dots (1)$ .

Compare the given equation with standard form and conclude that width="92">x24+y216=1is in standard form.

Step 3. Find whether the major axis is horizontal or vertical.

Compare the equation $(1)$ with $\frac{x^{2}}{4} + \frac{y^{2}}{16} = 1$ to find $a^{2}$ and $b^{2}$ .

$\begin{array}{rcl} a^{2} & = & 4 \\ b^{2} & = & 16 \end{array}$

Since $16 > 4$ and $16$ is in the $y^{2}$ term, the major axis will be vertical.

Step 4. Find the endpoints of the major axis.

The endpoints will be the $y$ -intercepts.

Since $b^{2} = 16$ , $b = \pm 4$ .

Thus, the coordinates of the endpoints of the major axis are role="math" localid="1645594892127" $(0, 4)$ and role="math" localid="1645594900062" $(0, - 4)$ .

Step 5. Find the endpoints of the minor axis.

The endpoints will be the $x$ -intercepts.

Since $a^{2} = 4$ , $a = \pm 2$ .

Thus, the coordinates of the endpoints of the minor axis are $(2, 0)$ and $(- 2, 0)$ .

Step 6. Draw the ellipse.

The graph of an ellipse is shown below:

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Graph: $\frac{x^{2}}{4} + \frac{y^{2}}{16} = 1$ .

Short Answer

Step by step solution

Given Information

Step 2. Write the equation in standard form.

Step 3. Find whether the major axis is horizontal or vertical.

Step 4. Find the endpoints of the major axis.

Step 5. Find the endpoints of the minor axis.

Step 6. Draw the ellipse.

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Graph: x24+y216=1.

Short Answer

Step by step solution

Given Information

Step 2. Write the equation in standard form.

Step 3. Find whether the major axis is horizontal or vertical.

Step 4. Find the endpoints of the major axis.

Step 5. Find the endpoints of the minor axis.

Step 6. Draw the ellipse.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Pure Maths

Mechanics Maths

Statistics

Theoretical and Mathematical Physics

Geometry

Study anywhere. Anytime. Across all devices.

Graph: $\frac{x^{2}}{4} + \frac{y^{2}}{16} = 1$ .