Chapter 3.7, Problem 67E

Consider the tangent line to the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ at a point (p, q) in the first quadrant.

(a) Show that the tangent fine has x-intercept $a^2/p$ and y –intercept $b^2/p$.

(b) Show that the portion of the tangent line cut off by the coordinate axes has minimum length a + b.

(c) Show that the triangle formed by the tangent line and the coordinate axes has minimum area ab.