Question

The curve with parametric equations $x=1+4cos\theta ,y=2+3sin\theta$ is

• A. an ellipse
• B. a parabola
• C. a hyperbola
• D. a circle

Answer 1

The correct option is A an ellipse

We have, $x=1+4cos\theta ,y=2+3sin\theta$;
${\left(\frac{x-1}{4}\right)}^2+{\left(\frac{y-2}{3}\right)}^2=1$
or $\frac{(x-1{)}^2}{16}+\frac{(y-2{)}^2}{9}=1$, which is an ellipse.