Question

The formula for the area of an ellipse is Arnab. Using a + b = 20 write the area of
the ellipse as a function of a by solving for a and then plugging in your results
into the formula for the area of an ellipse to replace b.

Answer 1

$A=\pi ab\qquad \qquad \begin{array}{llll} a+b=20\\ b=20-a \end{array}\qquad \qquad \stackrel{\textit{substituting}}{A=\pi a(20-a)}\implies A=\pi (20a-a^2)$