Question

Find the co ordinates of a circle passing through the points P(6,-6),Q(3,-7),R(3,3).​

Answer 1

Answer:

Let the center of the circle be A(x,y)A(x,y)

Then PA=PQPA=PQ

PA^2=QA^2PA

2

=QA

2

(x-6)^2+(y+6)^2=(x-3)^2+(y+7)^2(x−6)

2

+(y+6)

2

=(x−3)

2

+(y+7)

2

3x+y-7=03x+y−7=0  --- (i)

AP=ARAP=AR

(AP)^2=(AR)^2(AP)

2

=(AR)

2

(x-6)^2+(y+6)^2=(x-3)^2+(y-3)^2(x−6)

2

+(y+6)

2

=(x−3)

2

+(y−3)

2

3x-9y-27=03x−9y−27=0  ---- (ii)

(ii) - (i), we get

y=-2y=−2

put in (i)

x=3x=3

Therefore center of the circle is (3,-2)(3,−2)

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