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

Answers ( )

    0
    2021-08-23T05:51:18+00:00

    Answer:

    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)

    Add (1) and (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

    PLS MARK IT AS BRAINLIEST

    Read more on Brainly.in – https://brainly.in/question/1146723#readmore

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