Chapter 10: Q 56. (page 655)

Find an equation for each ellipse. Graph the equation by hand.
Center at $(- 3, 1)$ : vertex at $(- 3, 3)$ : focus at $(- 3, 0)$

Short Answer

Expert verified

The equation of the ellipse is $\frac{{(x + 3)}^{2}}{3} + \frac{{(y - 1)}^{2}}{4} = 1$ graph of the ellipse is

Step by step solution

Step 1. Given information.

Center at $(- 3, 1)$ : Vertex at $(- 3, 3)$ : focus at $(- 3, 0)$ .

Since the center, focus and vertex all lies on the line $x = - 3$ the major axis is parallel to the y- axis.

The distance from the center of the ellipse to the focus is $c = 1$

The distance from the center of the ellipse to the vertex is $a = 2$

Step 2. The equation of ellipse.

Substitute $c = 1$ and $a = 2$ in $b^{2} = a^{2} - c^{2}$ we get.

$b^{2} = a^{2} - c^{2} b^{2} = 2^{2} - 1^{2} b^{2} = 4 - 1 b^{2} = 3$

The equation of the ellipse is $\frac{{(x + 3)}^{2}}{3} + \frac{{(y - 1)}^{2}}{4} = 1$

Step 3. Graph of the ellipse.

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Find an equation for each ellipse. Graph the equation by hand.
Center at $(- 3, 1)$ : vertex at $(- 3, 3)$ : focus at $(- 3, 0)$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. The equation of ellipse.

Step 3. Graph of the ellipse.

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Find an equation for each ellipse. Graph the equation by hand.Center at (-3,1): vertex at (-3,3): focus at(-3,0)

Short Answer

Step by step solution

Step 1. Given information.

Step 2. The equation of ellipse.

Step 3. Graph of the ellipse.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Pure Maths

Calculus

Statistics

Decision Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

Find an equation for each ellipse. Graph the equation by hand.
Center at $(- 3, 1)$ : vertex at $(- 3, 3)$ : focus at $(- 3, 0)$