Question

Find the centre of a circle passing through the points (6,-6), (3,-7) and (3,3).

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Answer 1

Answer:

Let O(x,y) is the center of the circle and A(6.−6),B(3,−7) and C(3,3)are the points on the circumference of the circle.

∴OA= (x 1 −x 2 ) 2 +(y 1−y 2 ) 2

OA= (x−6)

2 +(y+6) 2

OB= (x−3)

2 +(y+7) 2

OC= (x−3) 3 +(y−3) 2

∵ Radii of the circle are equal

∴OA=OB

(x−6)

2+(y+6)

2 = (x−3)

2 +(y+7)

2x

2+36−12x+y

2 +36+12y=x

2 +9−6x+y

2 +49+14y

−6x−2y+14=0

3x+y=7

Similarly,

OA=OC

(x−6)

2+(y+6)

2 = (x−3)

2 +(y−3)

2 x

2 +36−y+y

2 +36+12y=x

2 +9−6x+y

2 +9−6y

−6x+18y+54=0

−3x+9y=−27

Adding (i) and (ii)

10y=−20

y=−2

Substitute the value of y in (i)

3x+−2=7

3x=9

x=3

∴ The center of the circle is (3,−2).

Hope this helps you