Consider the tangent line to the ellipse

at a point (p, q) in the first quadrant.

(a) Show that the tangent line has x-intercept a²/p and y-intercept b²/q.

(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.

Transcribed Image Text:

x2 2 a + 2 b2 = 1