Question

Parametric equation of the circle, $x^2+y^2-2x+4y-11=0$ is $x=$ and $y=$ .

• A. $-2+4\cos \theta$
• B. $4+4\cos \theta$
• C. $1+4\cos \theta$
• D. $-2+4\sin \theta$

Answer 1

Answer: (C), (D)

The correct options are
C $1+4\cos \theta$
D $-2+4\sin \theta$

To write the parametric equation of circle, we have to know the centre and radius of the circle. If the centre is $(h,k)$ and radius is $r,$ the parametric equation of the circle is given by $x=h+r\cos \theta$ and $y=k+r\sin \theta$.
The centre of $x^2+y^2-2x+4y-11=0$ is $(1,-2)$ and radius is $\sqrt{1^2+(-2{)}^2-(-1)}=4$

$\Rightarrow$ Parametric equation is $x=1+4\cos \theta$ and $y=-2+4\sin \theta$