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Manipal MET2016MathematicsEllipse

Tangent to the ellipse x^2 32 + y^2 18 =1 having slope -3 4 meet the coordinate axis at A and B . Then, the area of A O B , where O is the origin, is

Options

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

Correct answer

C. 24 sq units

Step-by-step solution

Equation of tangent with the slope -3 4 is y= -3 4 x+C . According to condition of tangency, C= 32 ( -3 4 )^2+18 = 18+18 =6 array lrl & y & = -3 4 x+6 & 4 y+3 x & =24 array Since, it meet the coordinate axes in A and B . A (8,0) and B (0,6) Required area = 1 2 8 6=24 sq units

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