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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 (x+1)29+(y-2)25=1and graph of the ellipse is

Step by step solution

01

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)

02

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

b2=a2-c2b2=32-22b2=9-4b2=5

Substitute the value of a2and b2in the equation of ellipse, we get

(x+1)29+(y-2)25=1

03

.Graph of the ellipse 

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