# What information do you need to get algebraically, to graph a conic section?

Mar 7, 2015

There are additional questions asked about the graphs and the equations, but to get a good sketch of the graph:

You need to know whether the axes have been rotated. (You'll need trigonometry to get the graph if the have been.)

You need to identify the type or kind of conic section.

You need to put the equation in standard form for its type.

(Well, you don't "need" this to graph something like $y = {x}^{2} - x$, if you'll settle for a sketch based on it being an upward opening parabola with $x$-intercepts $0$ and $1$)

Depending on the type of conic, you'll need other information depending on how detailed you want your graph:

(Sometimes we are also interested in the parameter $p$, the focus, and the directrix.)
Hyperbola : center, directions of opening, $a$ and $b$ to find the asymptotes