# How do I graph the ellipse with the equation (x−4)^2/36+(y-3)^2/36=1?

Feb 6, 2015

First of all... this is not an ellipse, o better... this is a very particular ellipse. This is a circle!

An ellipse have an equation like this:

${\left(x - {x}_{c}\right)}^{2} / {a}^{2} + {\left(y - {y}_{c}\right)}^{2} / {b}^{2} = 1$, where $C \left({x}_{c} , {y}_{c}\right)$ is the center, $a$ is the orizontal semi-axis and $b$ is the vertical semi-axis.

But... if $a = b$, the semi-axes are equal and so it is a circle.

In our case:

${\left(x - 4\right)}^{2} / 36 + {\left(y - 3\right)}^{2} / 36 = 1 \Rightarrow {\left(x - 4\right)}^{2} + {\left(y - 3\right)}^{2} = 36$ is the equation of a circle with centre $C \left(4 , 3\right)$ and radius $6$, and thisis its graph:

graph{(x-4)^2+(y-3)^2=36 [-20, 20, -10, 10]}