A Perpendicular-Bisector Locus

★ 7/10Circles conic sections analytic geometry

Problem

An ellipse $C$ has eccentricity $\dfrac{1}{2}$ and foci $F_1(-1, 0)$ , $F_2(1, 0)$ .

1. Find the equation of $C$ . 2. Let $M_0(1, 4)$ . Prove that the perpendicular bisector of segment $F_1M_0$ has exactly one point in common with $C$ . 3. Let $M$ be a moving point in the plane such that the perpendicular bisector of segment $F_1M$ has exactly one point in common with $C$ . Prove that the locus of $M$ is a circle, and find its equation.

Answer

Solution

Difficulty	7/10
Topics	Circles, 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.