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Tangents drawn from the point P(1,8) to ...

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&B ifR is the radius of circum circle of triangle PAB then [R]-

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-20`

D

`x^(2)+y^(2)-6x-4y+19=0`

Text Solution

Verified by Experts

The correct Answer is:
2
The center of the circle is `C( 3,2)`

Since CA and CB are perpendicular to PA and PB ,CP is the diameter of the circumcircle of triangle PAB. Its equation is
`(x-3)(x-1)+(y-2)(y-8)=0`
or `x^(2)+y^(2)-4x-10y+19=0`
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Tangents drawn from P(1,8) to the circle x^(2)+y^(2)-6x-4y-11=0 touches the circle at the points A and B, respectively.The radius of the circle which passes through the points of intersection of circles x^(2)+y^(2)-2x-6y+6=0 and x^(2)+y^(2)-2x-6y+6=0 the circumcircle of the and interse Delta PAB orthogonally is equal to