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AP EAMCET202423 May 2024Morning ShiftMathematicsStraight LinesActual

If the straight line passing through P(3,4) makes an angle 6 with the positive x -axis in anticlockwise direction and meets the line 12 x+5 y+10=0 at Q , then the length of the segment PQ is

Options

  1. A64 12 2 1
  2. B96 9 2 -1
  3. C112 10 3 +3
  4. D132 12 3 +5

Correct answer

D. 132 12 3 +5

Step-by-step solution

Any line through P(3,4) making an angle with x -axis is x-3 30^ = y-4 30^ =r Any point Q on it is ( r 3 2 +3, r 2 +4 ) and Q lies on 12 x+5 y+10=0 aligned & 12 [ ( r 3 2 )+3 ]+5 ( r 2 +4 )+10=0 & r= 132 12 3 +5 = length of segment P Q aligned

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