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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

  1. A \(\frac{2}{\sqrt{5}}\)
  2. B \(\frac{1}{\sqrt{5}}\)
  3. C 1
  4. D \(\frac{\sqrt{17}}{2}\)
Verified Solution

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:…