AP EAMCET · Maths · Circle
The radius of the circle whose diameter is the common chord of the circles \(x^2+y^2+2 x+2 y+1=0\) and \(x^2+y^2+4 x+3 y+2=0\) is
- A \(\frac{2}{\sqrt{5}}\)
- B \(\frac{1}{\sqrt{5}}\)
- C 1
- D \(\frac{\sqrt{17}}{2}\)
Answer & Solution
Correct Answer
(B) \(\frac{1}{\sqrt{5}}\)
Step-by-step Solution
Detailed explanation
Equation of common chord: \((x^2+y^2+2x+2y+1) - (x^2+y^2+4x+3y+2) = 0 \Rightarrow 2x+y+1=0\) Center of first circle: \(C_1 = (-1, -1)\) Radius of first circle: \(r_1 = \sqrt{(-1)^2 + (-1)^2 - 1} = \sqrt{1} = 1\) Distance from \(C_1\) to chord:…
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