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AP EAMCET202319 May 2023Morning ShiftMathematicsStraight LinesActual

If O is the origin and P, Q are points on the line 3 x+4 y+15=0 such that OP = OQ =9 , then the area of OPQ is

Options

  1. A6 2
  2. B9 2
  3. C12 2
  4. D18 2

Correct answer

D. 18 2

Step-by-step solution

Let M be the foot of perpendicular drawn from O(0,0) on line 3 x+4 y+15=0 Hence O M= | 3 0+4 0+15 3^2+4^2 |=3 Now since O M Q , M Q= 81-9 =6 2 Area of O P Q=2[ Area of O M Q] aligned & =2 [ 1 2 (O M)(M Q) ] & =3 6 2 =18 2 aligned

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