JEE Mains · Maths · STD 11 - 10.1 circle and system of circle
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 ..... .
- A \(1\)
- B \(\frac{1}{2}\)
- C \(\frac{1}{3}\)
- D \(\frac{1}{4}\)
Answer & Solution
Correct Answer
(B) \(\frac{1}{2}\)
Step-by-step Solution
Detailed explanation
\(h =\frac{\cos \theta+3}{2}\) \(k =\frac{\sin \theta+2}{2}\) \(\Rightarrow\left( h -\frac{3}{2}\right)^{2}+( k -1)^{2}=\frac{1}{4}\) \(\Rightarrow r =\frac{1}{2}\)
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