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TS EAMCET · Maths · Circle

The equation of the circle which touches the circle \(x^2+y^2-6 x+6 y+17=0\) externally and having the lines \(x^2-3 x y-3 x+9 y=0\) as two normals, is

  1. A \(x^2+y^2-2 x+5 y-1=0\)
  2. B \(x^2+y^2+2 x+3 y+1=0\)
  3. C \(x^2+y^2-6 x-2 y+1=0\)
  4. D \(x^2+y^2+4 x-3 y+3=0\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(x^2+y^2-6 x-2 y+1=0\)

Step-by-step Solution

Detailed explanation

Equation of normals \[ \begin{aligned} x^2-3 x y-3 x+9 y & =0 \\ \Rightarrow x(x-3 y)-3(x-3 y) & =0 \\ \Rightarrow \quad(x-3 y)(x-3) & =0 \end{aligned} \] So, equation of normals is \(x-3 y=0\) and \(x-3=0\) intersection of two normal is centre. So, \(x-3 y=0\) and \(x=3\).…