Question

The parametric coordinates of the circle whose center coordinates are $(-4,3)$ and touches the $y$-axis, is

• A. $x=-4+4\cos \theta ,y=3+4\sin \theta$
• B. $x=-4+4\cos \theta ,y=-3+4\sin \theta$
• C. $x=4-4\cos \theta ,y=3+4\sin \theta$
• D. $x=4+4\cos \theta ,y=3+4\sin \theta$

Answer 1

The correct option is A $x=-4+4\cos \theta ,y=3+4\sin \theta$

As the given circle touches the $y$-axis, therefore perpendicular distance between the $y$-axis and center $(-4,3)$ is the radius $\left(r\right)$.
$\therefore r=4$

As we know parametric form for the circle $(x-h{)}^2+(y-k{)}^2=r^2$ is
$x=h+r\cos \theta ,y=k+r\sin \theta$
So, the required parametric coordinates will be
$x=-4+4\cos \theta ,y=3+4\sin \theta$