How do you go about plotting x^2- y^2=0 for [-3, 3]

Ok, if you solve it for Y and plot it you get ONE straight line. Supposedly, there has to be another one crossing the 2nd and 4th quadrants. I am confused. Please, do tell me what I am failing to see here.

Thanks.

y^2= x^2
y= + sqrt x^2 AND y=-sqrtx^2
therefore for any given y you will get two different answers for x.
This is not a straight line.