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P is a variable point on the ellipse fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction+fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction= 1 with AA' as the major axis. Then, the maximum value of the area of the triangle APA' is-wor

  1. ab    
  2. 2ab    
  3. ab/2    
  4. None of these    

hintHint:

find out the area in terms of  the parametric coordinates and find the maxima.

The correct answer is: ab


    ab
    let the point P be (a cos t, b sin t)
    area of triangle APA’ = ½ (2a)(bsint) = ab sin t
    to find the maxima, we need to differentiate the above function
    we get, ab cos(t) = 0
    t=90
    hence, maximum area = ab sin 90 = ab

    when we differentiate an expression, we get the critical points where either maxima or minima can exist.

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