Question

Explain parametric equation of a circle.

Answer 1

Equation of the circle
$=(x-h{)}^2+(y-k{)}^2=r^2$
Where centre (h,k) and radius ‘r’

Every point p on the circle can be represented as $x=h+rcos\theta y=k+rsin\theta$. Where $\theta$ in the parameter.
$(x-h{)}^2+(y-k{)}^2=r^2$
$(h+rcos\theta -h{)}^2+(k+rsin\theta -k{)}^2=r^2$
$r^{2}co{s}^2\theta +r^{2}si{n}^2\theta +r^2$
$÷r^2$
$co{s}^2\theta +si{n}^2\theta =1$
1 = 1
$\Rightarrow x=h+rcos\theta$ and $y=k+rsin\theta$ $0\le \theta \le 2\pi$ in the parametric equation of circle where $\theta$ in the parameter.