# 8) Find the maximum area of an isosceles triangle inscribed in the ellipse  with its vertex at one end of the major axis.

Given the equation of the ellipse

Now, we know that ellipse is symmetrical about x and y-axis. Therefore, let's assume coordinates of A = (-n,m) then,
Now,
Put(-n,m) in equation of ellipse
we will get

Therefore, Now
Coordinates of A =
Coordinates of B =
Now,
Lenghth AB(base) =
And height of triangle ABC = (a+n)
Now,
Area of triangle =

Now,

Now,

but n cannot be zero
therefore,
Now, at

Therefore,  is the point of maxima
Now,

Now,
Therefore,  Area (A)

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