Three forms of tangent to $y^2$ = 4ax:

1. Point form (T=0): yy1 = 2a(x + x1) at point (x1, y1)
2. Slope form: y = mx + a/m for slope m (m not 0)
3. Parametric: ty = x + $at^2$ at parameter t

The slope form reveals that for any non-zero slope m, there is exactly one tangent to the parabola. The point of tangency for slope m is (a/$m^2$, 2a/m).