# How do you graph an ellipse written in general form?

Oct 31, 2014

Graphing the general picture of an ellipse given an equation is relatively simple work. It's all about interpretation.

Let's start by looking at our standard ellipse equations:

${\left(x - h\right)}^{2} / {a}^{2} + {\left(y - k\right)}^{2} / {b}^{2}$ (Horizontal Ellipse)

${\left(x - h\right)}^{2} / {b}^{2} + {\left(y - k\right)}^{2} / {a}^{2}$ (Vertical Ellipse)

$a$ and $b$ simply describe the distance from the centre that the ellipse goes.

The one under $x$ is the distance it travels vertically, while the one under $y$ is the distance it travels horizontally. Do not be intimidated by the $b$ and $a$; they simply tell you which one is longer ($a$ is always longer than $b$).

Also, $h$ and $k$ give you the coordinates for your vertex. $\left(h , k\right)$ is your vertex.

Now all you need to do is take your centre, and measure out $a$ and $b$ distance in the appropriate directions, connect the dots, and you are done. Just make sure that you square root your $a$ and $b$ before using them, and that you're using them in the right direction ($x$ or $y$). Also watch out for the signs of your $h$ and $k$.

Hope that helped :)