# How do you name the curve given by the conic r=6?

Dec 9, 2016

It is a circle with center at $\left(0 , 0\right)$ and radius $6$.

#### Explanation:

$r = 6$ denotes locus of a point which moves so that it's distance from origin is always constant and at $6$.

It is quite apparent that this is the equation of a circle with center at origin and radius$6$.

Further, relation between polar coordinates $\left(r , \theta\right)$ and Cartesian coordinates $\left(x , y\right)$ is given by $x = r \cos \theta$ and $x = r \sin \theta$ i.e. ${r}^{2} = {x}^{2} + {y}^{2}$.

Hence, $r = 6$ on squaring translates into ${x}^{2} + {y}^{2} = 36$ and is equation of circle with center at $\left(0 , 0\right)$ and radius is $6$.