Question

The centre of the circle $x=1+2\cos \theta ,y=-3+2\sin \theta ,$ is

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

Answer 1

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

Given,
$\frac{x-1}{2}=\cos \theta ,\frac{y+3}{2}=\sin \theta$
squaring and adding both the equations, we get

${\left(\frac{x-1}{2}\right)}^2+{\left(\frac{y+3}{2}\right)}^2=1$
$\Rightarrow (x-1{)}^2+(y+3{)}^2=2^2$

Hence, centre of circle is $(1,-3)$