?Consider the tangent line to the ellipse + = 1 at a point (????, ????) in the first

Chapter 4, Problem 73

(choose chapter or problem)

Consider the tangent line to the ellipse + = 1 at a point (𝑝, π‘ž) in the first quadrant.

(a) Show that the tangent line has π‘₯-intercept π‘Ž2/𝑝 and 𝑦-intercept 𝑏2/π‘ž.

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

(c) Show that the triangle formed by the tangent line and the coordinate axes has minimum area π‘Žπ‘.

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