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Let A B be chord of contact of the point...

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`

Text Solution

Verified by Experts

The correct Answer is:
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`
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