Answer A) Ellipse
x=a cos t
or, x^{2}=a^{2}cos^{2}t
or, $\frac{x^2}{a^2}$ =cos^{2}t.......................i
y=b sin t
or,y^{2}=b^{2}sin^{2}t
or,$\frac{y^2}{b^2}$ = sin^{2}t........................ii
from i and ii
$\frac{x^2}{a^2}$ +$\frac{y^2}{b^2}$ =cos^{2}t+sin^{2}t =1