Question

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

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

Answer 1

Answer: (B)

(–1, 3)

Answer 2

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 $( - 1,3 )$ .