Question

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

• A. $(2--3)$
• B. $(-1,3)$
• C. $(1,3)$
• D. None of these

Answer 1

Answer: (B)

$(-1,3)$

$\Rightarrow x=-1+2cos\Theta ,y=3+2sin\Theta$

$\frac{x+1}{2}=cos\Theta ,\frac{y-3}{2}=sin\Theta$

we know that

$co{s}^2\Theta +si{n}^2\Theta =1$

$\frac{(x+1{)}^2}{4}+\frac{(y-3{)}^2}{4}=1$

$\Rightarrow (x+1{)}^2+(y-3{)}^2=4$ center is (-1,3)