Question

find the area enclosed by the curve x=3cost, y=2sint

Answer 1

These are parametric equations of ellipse
$\frac{ {x}^{2} }{ {a}^{2} } + \frac{ {y}^{2} }{ {b}^{2} } = 1$
Its parametric equations are
x = a cost y= b sint

Area enclosed by the ellipse

=
$\pi \: a \: b$

$6\pi$