A Distance-Ratio Locus

★ 5/10Substitution conic sections analytic geometry Casework

Problem

A moving point $M(x, y)$ has distance to the line $l \colon x = 4$ equal to twice its distance to the point $N(1, 0)$ .

1. Find the equation of the locus $C$ of $M$ . 2. A line $m$ through $P(0, 3)$ meets $C$ at two points $A$ and $B$ . If $A$ is the midpoint of $PB$ , find the slope of $m$ .

Answer

Solution

Difficulty	5/10
Topics	Substitution, conic sections, analytic geometry, Casework

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