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Tangents PT1, and PT2, are drawn from a ...

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 lies on the line `Px +qy + r = 0`, then the locus of the centre of circumcircle of the triangle `PT_1T_2` is

A

A. `px +qy = r`

B

B. `(x-p)^(2)+(y-q)^(2) =r^(2)`

C

C. `px +qy =(r)/(2)`

D

D. `2px +2qy +r = 0`

Text Solution

Verified by Experts

The correct Answer is:
D
`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`.
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