Question

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

• A. (3,3)
• B. (2, -1)
• C. (- 2, 1)
• D. (- 1, 2)

Answer 1

Answer: (B)

(2, -1)

Answer 2

Given parametric equations are
$x=2+3 \cos \theta, y=3 \sin \theta-1$
or $\cos \theta=\frac{x-2}{3}, \sin \theta=\frac{y+1}{3}$
Since, $\sin ^{2} \theta+\cos ^{2} \theta=1$
$\Rightarrow\left(\frac{x-2}{3}\right)^{2}=\left(\frac{y+1}{3}\right)^{2}=1$
$\Rightarrow(x-2)^{2}+(y+1)^{2}=3^{2}$
$\therefore$ Centre of circle is $(2,-1)$.