Consider the circle `x^2+y^2-10x-6y+30=0`. Let O be the centre of the circle and tangent at A(7,3) and B(5, 1) meet at C. Let S=0 represents family of circles passing through A and B, thenA. the area of quadrilateral OACB is 4B. the radical axis for the famil of circles of `S=0` is `x+y=0`C. the smallest possible circle of the family `S=0` is `x+y-12x-4+38=0`D. the coordinates of point C are (7,1)

Consider the circle `x^2+y^2-10x-6y+30=0`. Let O be the centre of the

1.	Consider the circle `x^2+y^2-10x-6y+30=0`. Let O be the centre of the circle and tangent at A(7,3) and B(5, 1) meet at C. Let S=0 represents family of circles passing through A and B, thenA. the area of quadrilateral OACB is 4B. the radical axis for the famil of circles of `S=0` is `x+y=0`C. the smallest possible circle of the family `S=0` is `x+y-12x-4+38=0`D. the coordinates of point C are (7,1)
Answer» Correct Answer - 1,3,4 The coordinates of O are (5,3) and the radius is 2. The equation of tangent at A(7,3) is `7x+3y-5(x+7) -3(y+3) +30=0` `i.e., 2x-14=0` `i.e., x=7` The equation of tangent at `B (5,1)` is `5x+y-5(x+5)-3(y+1)+30=0` i.e., `-2y+2=0` i.e., `y=1` Therefore, the coordinates of C are (7,1) . So, area of OACB `=4` The equation of AB is `x-y=4` (radical axis). The equaiont of the smallest circle is `(x-7)(x-5)+(y-3)(y-1)=0` i.e., `x^(2)+y^(2)-12x-4y+38=0`

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