Question
Let P be a variable point on the ellipse 
+ 
= 1 with foci F1 and F2. If A is the area of the triangle PF1 F2, then the maximum value of A is-
- 2abe
- abe
abe
- None of these
abe
Hint:
assume an arbitrary point on the curve and find the value of A
The correct answer is: abe
abe
Let p be (a cos t , b sin t)
focii are (ae,0) and (-ae,0)
Area A = ½(bsin t x 2ae) = abe sin t
This is maximum when sin t = 1
Maximum value of A is abe
Area of triangle with given vertices can be calculated using the matrix determimnant method.
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