Question

The area of an ellipse is A = πab, but the perimeter cannot be expressed so simply:
P≈ π(a+b)(3-(√(3a+b)(a+3b))/(a+b) )
prove that, when a=b=r, these become the familiar formulas for the area and perimeter of a circle

Answer 1

Try replacing all the b's with a. eg in the area: A = πab becomes \[A = πaa = πa^2 = \pi r^2 \]
P will become:
\[P≈ π(a+a)(3-(√(3a+a)(a+3a))/(a+a) ) \] now try simplifying that.