The original worked lessons remain the main explanations. Use these focused reminders to check the conditions before you start.
Tangents, normals and complete line equations
Find the point and gradient before writing a line equation.
Treat a zero-gradient tangent and its vertical normal separately.
Find every permitted contact point, not just one.
At \(P(a,f(a))\), the tangent is \(y-f(a)=f^{\prime}(a)(x-a)\). For \(m\ne0\), the normal gradient is \(\displaystyle - \frac{1}{m}\). If \(m=0\), the normal is \(x=a\). An external point need not be a point of contact.