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  • Tangents PA and PB are drawn to circle <img alt="\mathrm{(x+4)^2+(y-4)^2=1}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B%28x&plus;4%29%5E2&plus;%28y-4%29%5E2%3D1%7D" /

Tangents PA and PB are drawn to circle \mathrm{(x+4)^2+(y-4)^2=1} from variable points P on xy = 1. The locus of circumcentre of triangle PAB is

Option: 1

 (2 x − 4) (2 x − 4) = 1


Option: 2

(2 x + 4) (2 y − 4) = 1


Option: 3

 (2 x + 4) (2 y + 4) = 1


Option: 4

 none of these


Answers (1)

best_answer

Locus is mid point of P and centre of circle

\mathrm{\begin{aligned} & \Rightarrow x=\frac{-4+t}{2} \\ & y=\frac{4+1 / t}{2} \\ & \Rightarrow(2 x+4)(2 y-4)=1 \end{aligned}}

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