A Vertex Distance Bound

★ 6/10Quadratic Equations conic sections analytic geometry

Problem

Let $B$ be the top vertex of the ellipse $C \colon \dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1$ (with $a > b > 0$ ). If every point $P$ on $C$ satisfies $|PB| \leqslant 2b$ , find the range of possible eccentricities of $C$ .

Answer

Solution

Difficulty	6/10
Topics	Quadratic Equations, conic sections, analytic geometry

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.