(a) Find the equation of the tangent at the point (1, 1) to the parabola y = x². Show that it is parallel to the line through the points (1/2, 1/4), (3/2, 9/4), which also lie on the parabola.

(b) Find the equation of the tangent at the point (a, a2) to the parabola y = x². Show that it is parallel to the line through the points (a – h, (a – h)²), (a + h, (a + h)²).