Question

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

The correct option is C $x=\cos \theta -1,y=2\sin \theta +1$

$4{(x+1)}^2+{(y-1)}^2=4\frac{{(x+1)}^2}{1}+\frac{{(y-1)}^2}{4}=1\Rightarrow a=1,b=2$

Now the standard parametric form is

$x=a\cos \theta ,y=b\sin \theta \Rightarrow x+1=\cos \theta ,y-1=2\sin \theta \Rightarrow x=\cos \theta -1,y=2\sin \theta +1$

So, option C is correct.