Posts tagged 'tangent'

W.21 Taylor Conics, Algebraic Tangents & Optical Reflection Laws

Translating any conic f(x, y) = 0 to a point A = [x_0, y_0] on the conic isolates a unique linear term l_1(x - x_0, y - y_0) = 0 defining its algebraic tangent t_tan without limits; for a parabola, t_tan is the perpendicular bisector of focus F_0 and directrix foot D_0 (giving equal spreads with F_0 A and the axis), and for a quadrola, t_tan makes equal spreads with both focal lines F_1 P_q and F_2 P_q.