If the locus of the mid-point

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 radius $r$, then $r$ is equal to :

  1. 1

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

  3. $\frac{1}{3}$

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


Correct Option: , 2

Solution:

$h=\frac{\cos \theta+3}{2}$c

$\mathrm{k}=\frac{\sin \theta+2}{2}$

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

$\Rightarrow \mathrm{r}=\frac{1}{2}$

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