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Chapter 11: Q. 11.13 (page 1077)

Write the standard form of the equation of the circle with center (2,1) that also contains the point (鈭�2,鈭�2).

Short Answer

Expert verified

The standard form of the equation of the circle is (x-2)2+(y-1)2=25.

Step by step solution

01

Step 1. Given information.

The center of the circle is (2,1).

The circle also contains the point (鈭�2,鈭�2).

We have to write the standard form of the equation of this circle.

02

Step 2. Use the Distance Formula to find he radius

Distance formula is (x2-x1)2+(y2-y1)2.

Substitute the values

localid="1645253431095" (x1,y1)=(2,1))(x2,y2)=(-2,-2)

Therefore, radius

r=(-2-2)2+(-2-1)2=(-4)2+(-3)2=16+9=25=5
03

Step 3. Write the standard form of circle

Put (h,k)=(2,1)r=5in the equation role="math" localid="1645253912371" (x-h)2+(y-k)2=r2.

role="math" localid="1645253812528" (x-2)2+(y-1)2=52(x-2)2+(y-1)2=25

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