MATHEMATICS · Multi-part · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices
Problem
For the curve given by x=3t2+1,y=2t3−t, answer the following.
(i) Find the coordinates of the point on the curve corresponding to t=1.
(ii) Determine the equations of the tangent and the normal lines to the curve at that point, writing each in slope–intercept form.
(iii) Eliminate the parameter to obtain an explicit Cartesian equation of each line found in part (ii).