Question

Tangents drawn from the point `P(1, 8)` to the circle `x^2+ y^2-6x-4y-11=0` touch the circle at the points `A` and `B`. The equation of the circumcircle of the triangle `PAB` is
(A) `x^2 +y^2 + 4x-6y + 19=0`
(B) `x^2 +y^2-4x-10y + 19=0`
(C) `x^2 + y^2-2x + 6y-29 = 0`
(D) `x^2 + y^2-6x-4y + 19 = 0`
A. `x^(2)+y^(2)+4x-6y+19=0`
B. `x^(2)+y^(2)-4x-10y+19=0`
C. `x^(2)+y^(2)-2x+6y-29=0`
D. `x^(2)+y^(2)-6x-4y+19=0`

Answer 1

For required circle, P(1, 8) and O(3 , 2) will be the end point of its diameter.
`therefore(x-1)(x-3)+(y-8)(y-2)=0`
`rArrx^(2)+y^(2)-4x-10y+19=0`