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TS EAMCET · Maths · Circle

For all real values of \(k\), the polar of the point (2k,k-4) with respect to \(x^2+y^2-4 x-6 y+1=0\) passes through the point

  1. A \((1,1)\)
  2. B \((1,-1)\)
  3. C \((-3,1)\)
  4. D \((3,1)\)
Verified Solution

Answer & Solution

Correct Answer

(D) \((3,1)\)

Step-by-step Solution

Detailed explanation

The polar of point \(P(2 k, k-4)\) with respect to the circle, \[ \begin{aligned} & x^2+y^2-4 x-6 y+1=0 \text { is } \\ & \begin{aligned} & 2 k x+y(k-4)+(-2)(x+2 k) \\ &+(-3)\{y+(k-4)\}+1=0 \\ & \Rightarrow k(2 x+y-7)-7 y-2 x+13=0 \end{aligned} \end{aligned} \] Hence, \((3,1)\)…