Horizontal tangents and vertical normals

A horizontal tangent at (a,b) is y=b and its perpendicular normal is x=a. A line perpendicular to a horizontal line is vertical; it has no finite gradient, so negative-reciprocal arithmetic cannot be used with zero. Method Differentiate before evaluating; if the tangent gradient is zero, write the normal directly as a constant-input line. Otherwise use the negative reciprocal. Example y=(x-2)2+1, y (2)=0 gives tangent y=1 and normal x=2. Exam check A vertical asymptote is outside the curve, not a vertical tangent. Where a vertical tangent is established geometrically, its normal is horizontal.