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If the angle between a pair of tangents drawn from a point $P$ to the circle $x^2+y^2-4 x+2 y+3=0$ is $\frac{\pi}{2}$ then, the locus of $P$ is
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Verified Answer
The correct answer is:
$x^2+y^2-4 x+2 y+1=0$
Given, equation of circle
$x^2+y^2-4 x+2 y+3=0$, Now required locus of point $P$ is $(x-2)^2+(y+1)^2=2(4+1-3)$
$\begin{aligned} & \Rightarrow \quad x^2+y^2-4 x+2 y+5=4 \\ & \Rightarrow \quad x^2+y^2-4 x+2 y+1=0\end{aligned}$
Hence, option (d) is correct.
$x^2+y^2-4 x+2 y+3=0$, Now required locus of point $P$ is $(x-2)^2+(y+1)^2=2(4+1-3)$
$\begin{aligned} & \Rightarrow \quad x^2+y^2-4 x+2 y+5=4 \\ & \Rightarrow \quad x^2+y^2-4 x+2 y+1=0\end{aligned}$
Hence, option (d) is correct.
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