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Chapter 10: Q. 46 (page 655)

Analyze each equation; that is, find the center, foci, and vertices of each ellipse. Graph each equation by hand. Verify your graph using a graphing utility.

9(x-3)2+(y+2)2=18

Short Answer

Expert verified

The center of ellipse is at (3,-2), vertices are (3,-2卤32)and the foci are (3,-2卤4)

The required graph is

Step by step solution

01

Step 1. Given Information 

The given equation is9(x-3)2+(y+2)2=18

02

Step 2. Calculation

Rewrite the given equation in the general form of equation,

9(x-3)2+(y+2)2=189(x-3)218+(y+2)218=1818(x-3)22+(y+2)218=1(x-3)22+(y-(-2))218=1

The major axis is parallel to y-axis.

Now, on comparing the obtained equation with the general form of equation, we get,

(h,k)=(3,-2)a2=18.b2=2c2=18-2c2=16c=4

The vertices of major axis are at

(h,k卤a)=(3,-2卤32)i.e.,(3,-2+32)and(3,-2-32)

And the foci are at point(h,k卤c)=(3,-2卤4)i.e.,(3,2)and(3,-6)

03

Step 3. Graph

On plotting all the points, we get the required graph,

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