Teach me about conics?

Question

I don't understand how to graph hyperbola conics?

Answer 1

 Say You have:

 

 

   X^2/ 4 - Y^2/ 9 =1  ( 1)

 

 

        First draw asymptotes  Y = -3/2 X ,  Y = 3/2 X

 

 

           Equation (1) doesn't have Y intercept.

          

             X intercept :   X = -2  X =+2

 

            So the Hyperbola will run a curvy shape with X intercepts ( -2 & +2) , and flattens  parallel with

           asymptotes.

 

           If it was  Y^2/9 - X ^2/ 4 =1   (2)

          

           (2)    It doesn't have x intercepts and do the same with Y intercepts ( 0,-3) & ( 0,+3).

 

                       ( X - a) ^2 / 9 - ( Y -b) ^2 =1

 

                     Center shifts to point (a, b).