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TS EAMCET · Maths · Circle

If a tangent to the circle \(x^2+y^2+2 x+2 y+1=0\) is radical axis of the circles \(x^2+y^2+2 g x+2 f y+c=0\) and \(2 x^2+2 y^2+3 x+8 y+2 c=0\), then

  1. A \(g=\frac{3}{7}\) or \(f=4\)
  2. B \(g=\frac{3}{2}\) or \(f=\frac{2}{3}\)
  3. C \(g=\frac{3}{5}\) or \(f=1\)
  4. D \(g=\frac{3}{4}\) or \(f=2\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(g=\frac{3}{4}\) or \(f=2\)

Step-by-step Solution

Detailed explanation

Equation of \(S_1\): \(x^2+y^2+2 x+2 y+1=0\) Center of \(S_1\): \(C_1 = (-1, -1)\) Radius of \(S_1\): \(R_1 = \sqrt{1^2+1^2-1} = 1\) Equation of \(S_2\): \(x^2+y^2+2 g x+2 f y+c=0\) Equation of \(S_3\): \(2 x^2+2 y^2+3 x+8 y+2 c=0 \Rightarrow x^2+y^2+\frac{3}{2} x+4 y+c=0\)…