# How do you graph x^2 + y^2 = 16?

Mar 13, 2018

This is a circle of radius $4$ centred at the origin.

#### Explanation:

Given:

${x}^{2} + {y}^{2} = 16$

Note that we can rewrite this equation as:

${\left(x - 0\right)}^{2} + {\left(y - 0\right)}^{2} = {4}^{2}$

This is in the standard form:

${\left(x - h\right)}^{2} + {\left(y - k\right)}^{2} = {r}^{2}$

of a circle with centre $\left(h , k\right) = \left(0 , 0\right)$ and radius $r = 4$

So this is a circle of radius $4$ centred at the origin:

graph{x^2+y^2 = 16 [-10, 10, -5, 5]}

Jul 7, 2018

See below:

#### Explanation:

The equation of a circle is given by

${\left(x - h\right)}^{2} + {\left(y - k\right)}^{2} = {r}^{2}$

With center $\left(h , k\right)$ and radius $r$.

We have no $h$ or $k$ term, so we know our circle is centered at the origin.

We know from $\sqrt{16}$ that our radius is $4$. Now, we have everything we need to graph!

graph{x^2+y^2=16 [-10, 10, -5, 5]}

Hope this helps!