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MHT CET2009MathematicsEllipse

Tangent to the ellipse x² 32 + y² 18 =1 having slope - 3 4 meet the coordinate axes in A and B . Find the area of the A O B , where O is the origin.

Options

  1. A12 sq unit
  2. B8 sq unit
  3. C24 sq unit
  4. D32 sq unit

Correct answer

C. 24 sq unit

Step-by-step solution

Equation of tangent with slope - 3 4 is y=- 3 4 x+c According to condition of tengency aligned c &= 32 ( -3 4 )²+18 &= 18+18 &=6 y &=- 3 4 x+6 aligned 4 y+3 x=24 It meets the coordinate axes in A and B . A (8,0) and B (0,6) Required area = 1 2 8 6=24 sq unit

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