# How do you graph x^2 + y^2 = 81?

Feb 22, 2016

It is an equation of a circle with centre at $\left(0 , 0\right)$ and radius $9$.

#### Explanation:

The equation is of the form of a circle with center at origin, as in the general form of a quadratic equation

$a {x}^{2} + 2 h x y + b {y}^{2} + 2 f x + 2 g y + c = 0$, while coefficients of ${x}^{2}$ and ${y}^{2}$ are equal (i.e. $a = b$), $f , g , h$ are all zeros. In fact equation ${x}^{2} + {y}^{2} = 81$ graph{x^2+y^2=81 [-20, 20, -10, 10]} can be written as

${\left(x - 0\right)}^{2} + {\left(y - 0\right)}^{2} = {9}^{2}$

and hence it is an equation of a circle with centre at $\left(0 , 0\right)$ and radius $9$.

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 $r$.

Since we have no $h$ or $k$ term, we know that we are centered at the origin.

From $\sqrt{81}$, we know that our radius is $9$. Now we can graph!

graph{x^2+y^2=81 [-20, 20, -10, 10]}

Hope this helps!