Finding the Equations of Tangents and Normals to Parametric Curves
Parametric curves take the formwhereis a parameter. Each value of gives (not necessarily unique) values ofandIf we need to find the equation of a tangent or normal to the curve at any pointthen we need the gradientat that point. We findusing the identitywill be a function ofso if we have the vale ofwe can findthe coordinatesthen useto find the equation of the tangent orto find the equation of the normal.
Example: Find the equation of the tangent and normal for the curve given in parametric coordinates asat
If we have the pointbut notthen we have to use the point to find
Example: Find the equation of the tangent and normal for the curve given in parametric coordinates asat the point
We have to find the value ofandFrom these two,