Question

Let `A B` be chord of contact of the point `(5,-5)` w.r.t the circle `x^2+y^2=5` . Then find the locus of the orthocentre of the triangle `P A B` , where `P` is any point moving on the circle.
A. `(x-3)^(2)+(y+3)^(2)=9`
B. `(x-3)^(2)+(y+3)^(2)=9//2`
C. `(x-3)^(2)+(y-3)^(2)=9`
D. `(x+3)^(2)+(y-3)^(2)=9//2`

Answer 1

Correct Answer - 1

The equation of AB is `x-y=3` (chord of contact)
Let orthocentre be `H(h,k)`.
Its image w.r.t. AB is `Q(k+3,h-3)`.
Q will lie on the circle `x^(2)+y^(2)=9`.
`:. (k+3)^(2)+(h-3)^(2)=9`
So, required locus is `(y+3)^(2)+(x-3)^(2)=9`