TS EAMCET · Maths · Circle
If a diameter of the circle \(x^2+y^2-4 x+6 y-12=0\) is a chord of a circle \(S\) whose centre is at \((-3,2)\), then the radius of \(S\) is
- A \(5 \sqrt {3}\)
- B \(4 \sqrt {3}\)
- C \(2 \sqrt {3}\)
- D \(5\)
Answer & Solution
Correct Answer
(A) \(5 \sqrt {3}\)
Step-by-step Solution
Detailed explanation
\(r=\sqrt{(2)^2+(-3)^2+12}=\sqrt{25}=5\) \(O C=\sqrt{(2+3)^2+(-3-2)^2}=5 \sqrt{2}\) \(\begin{array}{ll}\therefore & O P^2=r^2+O C^2=25+50=75 \\ \Rightarrow & O P=\sqrt{75}=5 \sqrt{3} .\end{array}\)
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