If the locus of the mid-point of the line segment
Question:

If the locus of the mid-point of the line segment from the point $(3,2)$ to a point on the circle, $x^{2}+y^{2}=1$ is a circle of the radius $r$, then $r$ is equal to:

  1. (1) $\frac{1}{4}$

  2. (2) $\frac{1}{2}$

  3. (3) 1

  4. (4) $\frac{1}{3}$


Correct Option: , 2

Solution:

$\therefore P \equiv(2 h-3,2 k-2) \rightarrow$ on circle

$\therefore\left(h-\frac{3}{2}\right)^{2}+(k-1)^{2}=\frac{1}{4}$

$\Rightarrow$ radius $=\frac{1}{2}$

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