TS EAMCET · Maths · Circle
A circle passes through the points \((2,0)\) and \((1,2)\). If the power of the point \((0,2)\) with respect to this circle is 4 , then the radius of the circle is
- A \(2\)
- B \(\sqrt{\frac{5}{2}}\)
- C \(\sqrt{5}\)
- D \(4\)
Answer & Solution
Correct Answer
(B) \(\sqrt{\frac{5}{2}}\)
Step-by-step Solution
Detailed explanation
Let the equation of circle be \(x^2+y^2+2 g x+2 f y+c=0\) \((2,0)\) and \((1,2)\) lies on it. \(\Rightarrow 4+4 g+c=0 \Rightarrow 4 g+c=-4\) ...(i) \(1+4+2 g+4 f+c=0 \Rightarrow 2 g+4 f+c=-5\) ...(ii) \(4=S_1^2=4+4 f+c \Rightarrow 4 f+c=0\) ...(iii) Solving (i), (ii) and (iii)…
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