Question

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

• A. An ellipse
• B. A parabola
• C. A hyperbola
• D. A circle

Answer 1

The correct option is A An ellipse

We have, $x=1+4\cos \theta ,y=2+3\sin \theta$

$\Rightarrow x-1=4\cos \theta ,y-2=3\sin \theta$

$\Rightarrow \frac{x-1}{4}=\cos \theta ,\frac{y-2}{3}=\sin \theta$
$\therefore {\left(\frac{x-1}{4}\right)}^2+{\left(\frac{y-2}{3}\right)}^2={\cos }^2\theta +{\sin }^2\theta$
$\Rightarrow \frac{(x-1{)}^2}{16}+\frac{(y-2{)}^2}{9}=1$
Which is an ellipse.