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Chapter 11: Q. 257 (page 1069)

In the following exercises, write the standard form of the equation of the circle with the given information:

Center is at(2,2)and a point on the circle is(4,4)

Short Answer

Expert verified

The equation of the circle isx2-4x+y2-4y=0

Step by step solution

01

Given information

The center of the circle is at(2,2)and a point on the circle is(4,4)

02

We use the distance formula to calculate the radius of the circle 

Let (x1,y1)=(2,2)(x2,y2)=(4,4)

The distance formula can be given as

r=(x1-x2)2+(y1-y2)2

Substituting the values we get

r=(4-2)2+(4-2)2r=22+22r=22

03

Use the standard form of the equation and substitute the corresponding values  

The standard form of the equation can be given as (x-h)2+(y-k)2=r2

Substituting the values we get

localid="1667920677793" (x-2)2+(y-2)2=(22)2x2-4x+4+y2-4y+4=8x2-4x+y2-4y=0

04

Conclusion

The equation of the circle isx2-4x+y2-4y=0

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