ExamBro
ExamBro
TS EAMCET · Maths · Circle

If \((4,2)\) and \((k,-3)\) are conjugate points with respect to \(x^2+y^2-5 x+8 y+6=0\), then \(k\) equals

  1. A \(\frac{28}{3}\)
  2. B \(-\frac{28}{3}\)
  3. C \(\frac{3}{28}\)
  4. D \(-\frac{3}{28}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{28}{3}\)

Step-by-step Solution

Detailed explanation

Equation of polar of point \((4,2)\) w.r.t. circle \[ \begin{aligned} & x^2+y^2-5 x+8 y+6=0 \text { is } T=0 \text {. } \\ & \therefore 4 x+2 y-\frac{5}{2}(x+4)+4(y+2)+6=0 \\ & \Rightarrow \quad 3 x+12 y+8=0 \\ & \end{aligned} \] Since, points \((4,2)\) and \((k,-3)\) are…