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Chapter 11: Q. 11.14 (page 1077)

Write the standard form of the equation of the circle with center (7,1) that also contains the point (-1,-5).

Short Answer

Expert verified

The standard form of the equation of the circle is (x-7)2+(y-1)2=100.

Step by step solution

01

Step 1. Given information.

The center of the circle is (7,1).

The circle also contains the point (-1,-5).

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

(x1,y1)=(7,1))(x2,y2)=(-1,-5)

Therefore, radius

r=(-1-7)2+(-5-1)2=(-8)2+(-6)2=64+36=100=10

03

Step 3. Write the standard form of circle

Put (h,k)=(7,1)r=10in the equation (x-h)2+(y-k)2=r2.

(x-7)2+(y-1)2=102(x-7)2+(y-1)2=100

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