AP EAMCET · Maths · Straight Lines
A straight line \(L\) cuts both the lines \(5 x-y-4=0\) and \(3 x+4 y-4=0\). The segment of \(L\) between the two lines is bisected at the point \((1,5)\). The equation of \(L\) is
- A \(63 x-32 y+62=0\)
- B \(36 x-53 y-72=0\)
- C \(38 x-65 y-45=0\)
- D \(83 x-35 y+92=0\)
Answer & Solution
Correct Answer
(D) \(83 x-35 y+92=0\)
Step-by-step Solution
Detailed explanation
Let the line L intersect \(5 x-y-4=0\) at \(A(x_1, y_1)\) and \(3 x+4 y-4=0\) at \(B(x_2, y_2)\). Given midpoint of AB is \((1,5)\): \(x_1 + x_2 = 2 \quad \text{and} \quad y_1 + y_2 = 10\) From line 1: \(y_1 = 5x_1 - 4\) From line 2: \(3x_2 + 4y_2 = 4\) Substitute…
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