# What information do you need to graph hyperbolas?

Mar 13, 2015

If It's known the equation of the hyperbolas, that is:

${\left(x - {x}_{c}\right)}^{2} / {a}^{2} - {\left(y - {y}_{c}\right)}^{2} / {b}^{2} = \pm 1$,

we can graph the hyperbolas in this way:

• find the center $C \left({x}_{c} , {y}_{c}\right)$;

• make a rectangle with the center in $C$ and with sides $2 a$ and $2 b$;

• draw the lines that pass from the opposite vertices of the rectangle (the asymptotes);

• if the sign of $1$ is $+$, than the two branches are left and right of the rectangule and the vertices are in the middle of the vertical sides, if the sign of $1$ is $-$, than the two branches are up and down of the rectangule and the vertices are in the middle of the horizontal sides.