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AP EAMCET · Maths · Straight Lines

The locus of the incentre of the triangle formed by the lines \(x y-4 x-4 y+16=0\) and \(x+y=5\) is

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

Answer & Solution

Correct Answer

(A) \(x-y=0\)

Step-by-step Solution

Detailed explanation

\(x y-4 x-4 y+16=0\) \(\begin{aligned} & x(y-4)-4(y-4)=0 \\ & (y-4)(x-4)=0\end{aligned}\) The 2 lines are \(x=4\) and \(y=4\) \(\begin{aligned} & \mathrm{L}_1: x=4 \\ & \mathrm{~L}_2: y=4 \\ & \mathrm{~L}_3: x+y=5\end{aligned}\)…