Question

The parametric form of the ellipse $4\left(x+1\right)^{2}+\left(y-1\right)^{2}=4$ is

• A. $x=\cos \theta-1, y=2 \,\sin \theta-1$
• B. $x=2 \cos \theta-1, y=\sin \theta+1$
• C. $x=\cos \theta-1, y=2 \sin \theta+1$
• D. $x=\cos \theta+1, y=2 \sin \theta+1$
• E. $x=\cos \theta+1, y=2 \sin \theta-1$

Answer 1

Answer: (C)

Given equation of ellipse can be rewritten as
$\frac{(x+1)^{2}}{1}+\frac{(y-1)^{2}}{4}=1$
$\therefore $ Parametric equations of ellipse is
$X+1=\cos \,\theta$
and $y-1 =2 \sin \,\theta$
$\Rightarrow x =\cos \,\theta-1 $
and $y=2 \sin \,\theta+1$