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) \[{{(x+3)}^{2}}+{{(y-3)}^{2}}=9/2\]
Correct Answer: A
Solution :
[a] 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 \[{{x}^{2}}+{{y}^{2}}=9.\] \[\therefore \,\,\,\,{{(k+3)}^{2}}+{{(h-3)}^{2}}=9\] So, required locus is \[{{(y+3)}^{2}}+{{(x-3)}^{2}}=9.\]You need to login to perform this action.
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