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Chapter 10: Q 60. (page 655)

Find an equation for each ellipse. Graph the equation by hand.

Vertices at(2,5)and(2,-1):c=2

Short Answer

Expert verified

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

Step by step solution

01

Step 1. Given information.  

Vertices at (2,5)and (2,-1): c=2

The vertices lies on the line x=2, thus the major axis is parallel to the y-axis.

The center is at the mid point of the vertices (2,2).

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.

02

Step 2. The equation of ellipse.  

Substitute a=3and c=2in b2=a2-c2we get.

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

Substituting the values of a2and b2in the equation of the ellipse we get.

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

03

.Graph of the ellipse .  

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