Question

Let P be a variable pointon the ellipse (x^2/25)+(y^2/16)=1 with foci at S and S'. If A be the area of triangle PSS', then the maximum value of A is ???

Answer 1

if it is algebra i can slove it srry bro

Answer 2

It is from Ellipse(Conic Section)...

Answer 3

a=5 b=4
Calculate eccentricity
\[e=\sqrt{1+b ^{2}/a ^{2}}\]
Then find the focus which is S(ae,0) and S'(-ae,0)
The area will be maximum when P is on the y-axis as shown in the diagram. So, coordinates of P will be (0,4)
Base is SS'=2ae
and Height = OP=4
Area=Base*Height/2
Did you understand it sid?