Question

The parametric equation $x=2+2cos\theta$ and $y=-2+2sin\theta$ represents

• A. A circle with centre (2, -2) and radius 2
• B. x² + y² - 4x + 4y + 4 =0
• C. A circle with centre (-2, 2) and radius 2
• D. x² + y² + 4x - 4y + 4 = 0

Answer 1

Answer: (A), (B)

The correct options are
A

A circle with centre (2, -2) and radius 2

B

x² + y² - 4x + 4y + 4 =0

We will eliminate $\theta$ using the identity $co{s}^2\theta +si{n}^2\theta =1$ to get the equation of the curve. We are given $x=2+2cos\theta$ and $y=-2+2sin\theta$

$(\frac{x-2}{2}{)}^2+(\frac{y+2}{2}{)}^2=si{n}^2\theta +co{s}^2\theta =1$

$\Rightarrow x^2+y^2-4x+4y+4=0\Rightarrow B$

This is a circle with centre $(2,-2)$ and radius 2.