Question

What information do you need to graph hyperbolas?

Answer 1

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

`(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)`;

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

• 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.