## The centre of the circle passing through (6,6), (3, -7) and (3, 3) is (1) (0, 0) (2) (-2, 3) (3) (3,-2) (4) (3, 2)​

Question

The centre of the circle passing through (6,6), (3, -7) and (3, 3) is
(1) (0, 0)
(2) (-2, 3)
(3) (3,-2)
(4) (3, 2)​

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3 weeks 2021-08-23T05:50:10+00:00 1 Answer 0 views 0

A(6,2) B(-1,3) C(-3,-1)

_________

OA = √(x-6)²+(y-2)²

________

OB = √(x+1)²+(y-3)²

_________

OC = √(x+3)²+(y+1)²

let O(x,y) be the centre of the circle.

OA=OB ( raddi of same circle )

_________ _________

=>√(x-6)²+(y-2)² = √(x+1)²+(y-3)²

squaring on both sides

=>(x-6)²+(y-2)² = (x+1)²+(y-3)²

=>x²+36-12x+y²+4-4y = x²+1+2x+y²+9-6y

=>36-12x+4-4y-1-2x-9+6y = 0

=>30-14x+2y = 0

=>30 = 14x-2y

=>7x-y = 15…………..(1)

OA=OC

_________ _________

=>√(x-6)²+(y-2)² = √(x+3)²+(y+1)²

squaring on both sides

=>(x-6)²+(y-2)² = (x+3)²+(y+1)²

=>x²+36-12x+y²+4-4y = x²+9+6x+y²+1+2y

=>36-12x+4-4y-9-6x-1-2y = 0

=>30-18x-6y = 0

=>30 = 18x+6y

=>5 = 3x+y…………..(2)

=>7x-y+3x+y = 15+5

=>10x = 20

=>x = 20/10 = 2

substitute x=2 in (2)

3x+y=5

=>3(2)+y = 5

=>y = 5-6 = -1

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

HOPE U UNDERSTAND

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