Tangents `PT_1, and PT_2`, are drawn from a point P to the circle `x^2 +y^2=a^2`. If the point P line `Px +qy + r = 0`, then the locus of the centre of circumcircle of the triangle `PT_1T_2` is

Options

A. `px +qy = r`
B. `(x-p)^(2)+(y-q)^(2) =r^(2)`
C. `px +qy =(r)/(2)`
D. `2px +2qy +r = 0`

Answer

D

Explanation

`P,T_(2),Q,T_(1)` are concylic points with PO as diameter.
Thus, the circumcentre of `DeltaPT_(1)T_(2)` is `((alpha)/(2),(beta)/(2))`.
New `(alpha, beta)` lies on `px +qy +r = 0`
i.e, locus of `((alpha)/(2),(beta)/(2))` is `2px +2qy +r =0`.