ExamBro
ExamBro
TS EAMCET · Maths · Circle

If \(5 x+6 y-34=0\) and \(2 x+y+c=0\) are conjugate lines with respect to the circle \(x^2+y^2-8 x-10 y+25=0\) then the point on the line \(2 x+y+c=0\) is

  1. A \((3,3)\)
  2. B \((2,4)\)
  3. C \((1,-5)\)
  4. D \((-2,-2)\)
Verified Solution

Answer & Solution

Correct Answer

(C) \((1,-5)\)

Step-by-step Solution

Detailed explanation

Given lines are \(5 x+6 y-34=0\) and \(2 x+y+C=0\) with respect to \(x^2+y^2-8 x-10 y+25=0\). \[ \begin{aligned} & x^2+y^2-8 x-10 y+25+16-16=0 \\ & \left(x^2-8 x+16\right)+\left(y^2-10 y+25\right)=16 \\ & (x-4)^2+(y-5)^2=(4)^2 \end{aligned} \] Here, centre is \((4,5)\) and…