Tangents and Normals to Conics

A tangent to a curve is a straight line touching it at exactly one point; the normal at that point is the line through it perpendicular to the tangent. Both were already built for the circle in §5.2.2–5.2.3 as limits of a chord ($Q\to P$) or via the perpendicular-distance-equals-radius condition; the same two techniques — chord-to-tangent limits, and "line meets curve in a repeated root" — now build the tangent and normal for the parabola, ellipse and hyperbola, in cartesian and parametric form, plus …