Point form: a^2x/x1 + b^2y/y1 = a^2 + b^2 = c^2. Note the + sign (contrast with ellipse which has -). Parametric: axcos(theta) + bycot(theta) = a^2 + b^2. Slope form: y = mx + m(a^2+b^2)/sqrt(a^2 - b^2*m^2). From an external point, at most 4 normals can be drawn. The normal at P bisects the angle between the focal radii SP and S'P.