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Chapter 11: Q. 8 (page 773)

Find the center and radius of the circlex2+y2-2x+4y-11=0. Graph the circle.

Short Answer

Expert verified

The center of the circle x2+y2-2x+4y-11=0is, 1,-2and the radius is, 4units.

The graph of the circle is,

Step by step solution

01

Step 1 Given equation is,

x2+y2-2x+4y-11=0.

The equation of the circle is, x-h2+y-k2=a2

where h,kis the center and ais the radius.

Now simplify the given equation to the form of the circle.

x2+y2-2x+4y-11=0x2-2x+y2+4y=11x2-2x+12+y2+4y+22=11+12+22x-12+y+22=11+1+4x-12+y+22=16x-12+y+22=42

02

Step 2 Now compare the obtained equation with the equation of the circle.

We get, the center is,1,-2and the radius is, 4.

Now let us draw a graph for the given equation of the circle whose center is marked by the point C.

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