Question

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

• A. (1, -3)
• B. (-1, 3)
• C. (1, 3)
• D. None of these

Answer 1

The correct option is B (-1, 3)

Given that $\frac{x+1}{2}=cos\theta .$
Also $\frac{y-3}{2}=sin\theta .$

$\Rightarrow {\left(\frac{x+1}{2}\right)}^2+{\left(\frac{y-3}{2}\right)}^2=1\Rightarrow (x+1{)}^2+(y-3{)}^2=4,$
whose centre is (-1, 3).