Chapter 10: Q 58. (page 655)

Find an equation for each ellipse. Graph the equation by hand.
Foci at $(1, 2)$ and $(- 3, 2)$ : vertex at $(- 4, 2)$ .

Short Answer

Expert verified

The equation of the ellipse is $\frac{{(x + 1)}^{2}}{9} + \frac{{(y - 2)}^{2}}{5} = 1$ and graph of the ellipse is

Step by step solution

Step 1. Given information.

Foci at $(1, 2)$ and $(- 3, 2)$ : vertex at $(- 4, 2)$ .

The focus and the vertex lie on the line $y = 2$ , so the major axis is parallel to the x-axis.

The center is at the midpoint of the foci $(h, k) = (- 1, 2)$

Step 2. The equation of ellipse.

The distance of the center from one of the foci is $c = 2$ .

The distance of the center from one of the vertices is $a = 3$

So, we have

$b^{2} = a^{2} - c^{2} b^{2} = 3^{2} - 2^{2} b^{2} = 9 - 4 b^{2} = 5$

Substitute the value of $a^{2}$ and $b^{2}$ in the equation of ellipse, we get

$\frac{{(x + 1)}^{2}}{9} + \frac{{(y - 2)}^{2}}{5} = 1$

.Graph of the ellipse

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Find an equation for each ellipse. Graph the equation by hand.
Foci at $(1, 2)$ and $(- 3, 2)$ : vertex at $(- 4, 2)$ .

Short Answer

Step by step solution

Step 1. Given information.

Step 2. The equation of ellipse.

.Graph of the ellipse

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Find an equation for each ellipse. Graph the equation by hand. Foci at(1,2)and(-3,2): vertex at(-4,2).

Short Answer

Step by step solution

Step 1. Given information.

Step 2. The equation of ellipse.

.Graph of the ellipse

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Decision Maths

Applied Mathematics

Pure Maths

Discrete Mathematics

Logic and Functions

Study anywhere. Anytime. Across all devices.

Find an equation for each ellipse. Graph the equation by hand.
Foci at $(1, 2)$ and $(- 3, 2)$ : vertex at $(- 4, 2)$ .