Question

Find the maximum area of an isosceles triangle inscribed in the ellipse x2a2+y2b2=1 with its vertex at one end of the major axis.

Answer 1

An ellipse is just a scaled down version of a circle. If the length of the major axis is 2a, that is, a>b, then the maximum area which can be inscribed is 3√3ab÷4. One of the methods to prove this is by using the parametric coordinates (a,0) , (acost, bsint) , and (acost, -bsint). Write the expression for ∆, differentiate it and equate it to zero. We get cost=1/2 and sint=√3/2. Thus, maximum area of a triangle inscribed in an ellipse is 3√3ab÷4.