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TS EAMCET · Maths · Circle

A circle passing through the points \((1,1)\) and \((2,0)\) touches the line \(3 x-y-1=0\). If the equation of this circle is \(x^2+y^2+2 g x+2 f y+c=0\), then a possible value of \(g\) is

  1. A \(-\frac{5}{2}\)
  2. B \(-\frac{3}{2}\)
  3. C \(6\)
  4. D \(-5\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(-\frac{5}{2}\)

Step-by-step Solution

Detailed explanation

\((1,1)\) and \((2,0)\) lie on circle. \(1+1+2 g+2 f+c=0 \Rightarrow 2 g+2 f+c=-2\) ...(i) \(4+4 g+c=0 \Rightarrow 4 g+c=-4\) ...(ii) (ii) - (i), \(2 g-2 f=-2 \Rightarrow f=(g+1) \Rightarrow C=-4-4 g\) Centre of circle is \((-g,-(g+1))\)…