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NTA Abhyas JEE Main2020MathematicsStraight LinesPractice

If the segment intercepted between the lines x + 6 y - 13 = 0 and x – y + 3 = 0 is bisected at 6,8 , then the square of the length of segment is

Options

  1. A268
  2. B244
  3. C212
  4. D252

Correct answer

B. 244

Step-by-step solution

Let the segment is A B as shown in the figure Let A = 13 - 6 y 1 , y 1 B = y 2 - 3 , y 2 ∴ mid-point A B = 6,8 ∴ 13 - 6 y 1 + y 2 - 3 2 = 6 . . . . . . . . . . . . . i And y 1 + y 2 2 = 8 . . . . . . . . . . . . . i i on solving i and i i we get A = 1,2 a n d B = 11,14 ⇒ ( A B ) 2 = 10 2 + 12 2 = 100 + 144 = 244

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