Question

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

Answer 1

It is a circle with center at `(0,0)` 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 `(r,theta)` and Cartesian coordinates `(x,y)` is given by `x=rcostheta` and `x=rsintheta` 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 `(0,0)` and radius is `6`.