Question
Let P be a variable point on the ellipse 
+ 
=1 with foci S and S'. If A be the area of triangle pss', then maximum value of A is–
- 12 sQ.units
- 24 sQ.units
- 36 sQ.units
- 48 sQ.units
Hint:
find the function of Area in terms of x and find the maxima by differentiating A with respect to x and equating it with 0
The correct answer is: 12 sQ.units
For the given ellipse, the value of e = √(1-b2/a2 )
e=3/5
foci: (ae,0),(-ae,0)
=> (3,0), (-3,0)
P: (x,y)
Vertices of triangle : (3,0),(-3,0) ,(x,y)
Area inside three vertices are:
area = 
Area = 12√(1-x2/25) as y=4√(1-x2/25)
For finding the maxima of Area,
dA/dx=0
this gives
-12x/25√(1-x2/25)=0
This gives x=0
Amax= 12(1-0) = 12 sq units.
the maxima or minima of a function is calculated by finding out the critical points of the function and then substituting the value of the critical point in the function.
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