Chapter 2, Problem 5PS

Tangent Lines and Normal Lines

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

(b) Find an equation of the normal line to $y=x^2$ 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 $y=x^2$ at the point (0,0).

(d) Prove that for any point (a, b) $\ne$

(0,0) on the parabola $y=x^2$, the normal line intersects the graph a second time.