Question

If $x=2+3\cos \theta$ and $y=1-3\sin \theta$ represent a circle then the centre and radius is?

• A. $(2,1),9$
• B. $(2,1),3$
• C. $(1,2),\frac{1}{3}$
• D. $(-2,-1),3$

Answer 1

The correct option is B $(2,1),3$

We have,
$x=2+3\cos \theta \Rightarrow 3\cos \theta \Rightarrow 3\cos \theta =x-2$ ..(i)
$y=1-3\sin \theta \Rightarrow 3\sin \theta =-y+1$ ..(ii)
Squaring adding (i) & (ii), we get
$(x-2{)}^2(-(y-1){)}^2=3^2({\cos }^2\theta +{\sin }^2\theta )$
$\Rightarrow (x-2{)}^2+(-(y-1){)}^2=3^2$
$\therefore$ Radius $=3$, centre $=(2,1)$.