Let a circle $C$ of radius 1 and closer to the origin be such that the lines passing through the point $(3,2)$ and parallel to the coordinate axes touch it. Then the shortest distance of the circle $\mathrm{C}$ from the point $(5,5)$ is :

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Aicharya · Accepted Answer

Coordinates of the centre will be $(2,1)$ Equation of circle will be $\begin{aligned} & (\mathrm{x}-2)^2+(\mathrm{y}-1)^2=1 \\ & \mathrm{QC}=\sqrt{(5-2)^2+(5-1)^2} \\ & \mathrm{QC}=5 \end{aligned}$ shortest distance $\begin{aligned} & =\mathrm{RQ}=\mathrm{CQ}-\mathrm{CR} \\ & =5-1 \\ & =4 \end{aligned}$

Let a circle $C$ of radius 1 and closer to the origin be such that the lines passing through the point $(3…

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