(a) Find an equation of the tangent line to the parabola y = x at the point...

(a) Find an equation of the tangent line to the parabola y = x² at the point (2, 4).

(b) Find an equation of the normal line to y = x² at the point (2, 4). (The normal line at a point is perpendicular to the tangent line at the point.) Where does this line intersect the parabola a second time?

(c) Find equations of the tangent line and normal line to y = x² at the point (0, 0).

(d) Prove that for any point (a, b) ≠ (0, 0) on the parabola
y = x², the normal line intersects the graph a second time.