Find the equation of a Hermite cubic spline that passes through points (1, 1) and (3, 2) and whose tangent vectors are as follows:
a. Tangent at (1,1): defined by line connecting (1,1) to (0,0)
b. Tangent at (3,2): defined by line connecting (3,2) to (4,2)
Sketch the curve and the blending functions for the defining points and vectors of a parametric cubic curve.