Let x(t) and y(t) be cubic Bzier curves with control points (p 0, p 1, p 2,

Let x(t) and y(t) be cubic Bézier curves with control points (p_0, p_1,p_2,p₃) and (p_3, p₄, p₅, p₆), respectively, so that x(t) and y(t) are joined at p³. The following questions refer to the curve consisting of x(t) followed by y(t). For simplicity, assume that the curve is in R².
a. What condition on the control points will guarantee that the curve has C₁ continuity at p₃? Justify your answer.
b. What happens when x'(1) and y'(0) are both the zero vector?