A Max Reciprocal Eccentricity Sum

★ 7/10Extrema Law of Cosines Cauchy-Schwarz conic sections

Problem

Let $F_1$ , $F_2$ be the common foci of an ellipse and a hyperbola, $P$ a common point of the two, with $\angle F_1PF_2=\dfrac{\pi}3$ . Find the maximum value of the sum of the reciprocals of the eccentricities of the ellipse and the hyperbola.

Answer

Solution

Difficulty	7/10
Topics	Extrema, Law of Cosines, Cauchy-Schwarz, conic sections

Whiteboard

Your sketch is saved only in this browser. To share it, export your drawing as an image (whiteboard menu → Export as → PNG), then upload that image in the comments below.

Discussion

Ask questions, share alternate solutions, and use LaTeX freely.

0 comments

No comments yet.