# How do you graph r = 2?

Dec 13, 2015

You can change it to rectangular coordinates or consider that is the graph produced by a point at distance $2$ from the origin and at all the possible angles $\theta$ from the positive $x$ axis (and so describing a circle!).

#### Explanation:

Consider the following diagram:

We can see that the relationships between rectangular and polar coordinates are:
$r = \sqrt{{x}^{2} + {y}^{2}}$
$\theta = \arctan \left(\frac{y}{x}\right)$
and:
$x = r \cos \left(\theta\right)$
$y = r \sin \left(\theta\right)$

$r = 2$
$\sqrt{{x}^{2} + {y}^{2}} = 2$
${x}^{2} + {y}^{2} = {2}^{2}$
Which is the equation of a circle of radius $2$ and centred in the origin.