What information do you need to graph hyperbolas?

1 Answer
Mar 13, 2015

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.