What information do you need to graph hyperbolas?

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Answer 1 · 2015-03-13T18:43:56

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

$\frac{{(x - x_{c})}_{c}^{2}}{a^{2}} - \frac{{(y - y_{c})}_{c}^{2}}{b^{2}} = \pm 1$ $(x-x_c)^2/a^2-(y-y_c)^2/b^2=+-1$ ,

we can graph the hyperbolas in this way:

find the center $C (x_{c}, y_{c})$ $C(x_c,y_c)$ ;
make a rectangle with the center in $C$ $C$ and with sides $2 a$ $2a$ and $2 b$ $2b$ ;
draw the lines that pass from the opposite vertices of the rectangle (the asymptotes);
if the sign of $1$ $1$ 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 $1$ $1$ is $-$ $-$ , than the two branches are up and down of the rectangule and the vertices are in the middle of the horizontal sides.