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AP EAMCET · Maths · Straight Lines

If the intercept of a straight line \(L\) made between the straight lines \(5 x-y-4=0\) and \(3 x+4 y-4=0\) is bisected at the point \((1,5)\), then the equation of \(L\) is

  1. A \(35 x-83 y+92=0\)
  2. B \(83 x+35 y-72=0\)
  3. C \(63 x-35 y+82=0\)
  4. D \(83 x-35 y+92=0\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(83 x-35 y+92=0\)

Step-by-step Solution

Detailed explanation

Let the line \(L\) intersect \(5x - y - 4 = 0\) at \(A(x_1, y_1)\) and \(3x + 4y - 4 = 0\) at \(B(x_2, y_2)\). Since \(P(1,5)\) is the midpoint of \(AB\): \(x_1+x_2=2\) and \(y_1+y_2=10\). From \(5x_1 - y_1 - 4 = 0 \implies y_1 = 5x_1 - 4\). Substitute \(x_2 = 2-x_1\) and…