Let (x1, y1) be the coordinates of a point on the parabola x2 = 4py. The equation of the line that just touches the parabola at the point (x1, y1), called a tangent line, is y − y1 = x1 / 2p (x − x1).
(a) What is the slope of the tangent line?
(b) For each parabola in Exercise 9, find the equations of the tangent lines at the endpoints of the chord. Use a graphing utility to graph the parabola and tangent lines.