Question

Find the parametric equation of the circle $x^2+y^2-2x+4y-11=0$

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

Answer 1

The correct option is D

$x=1+4cos\theta andy=-2+4sin\theta$

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 $x=h+rcos\theta andy=k+rsin\theta$.
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$x=1+4cos\theta andy=-2+4sin\theta$.