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99 Percentile Qs Bank for JEE MainMathematicsStraight Lines

The line 2 x + 3 y = 12 meets the coordinates axes at A and B respectively. The line through 5,5 perpendicular to A B meets the coordinate axes and the line A B at C , D and E respectively. If O is the origin, then the area (in sq. units) of the figure O C E B is equal to

Options

  1. A13 3
  2. B23 3
  3. C11
  4. D7

Correct answer

B. 23 3

Step-by-step solution

The equation of a line passing through P 5,5 and perpendicular to 2 x + 3 y = 12 is y - 5 = 3 2 x - 5 or, 3 x - 2 y - 5 = 0 The coordinates of the point of intersection of 2 x + 3 y - 12 = 0 and 3 x - 2 y - 5 = 0 are E 3,2 . The line 3 x - 2 y - 5 = 0 meets x -axis at C 5 3 , 0 . Now, A r e a o f f i g u r e O C E B = A r e a o f Δ A O B - A r e a o f Δ A C E = 1 2 O A × O B - 1 2 A C × E L = 1 2 × 6 × 4 - 1 2 × 13 3 × 2 = 23 3 s q . u n i t s

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