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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 (x+3)23+(y-1)24=1graph of the ellipse is

Step by step solution

01

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=-3the 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 isa=2

02

Step 2. The equation of ellipse. 

Substitute c=1and a=2in b2=a2-c2we get.

b2=a2-c2b2=22-12b2=4-1b2=3

The equation of the ellipse is(x+3)23+(y-1)24=1

03

Step 3. Graph of the ellipse.

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