An L-Distance Locus

★ 7/10Absolute Value analytic geometry Casework

Problem

In the coordinate plane, the L-distance between points $P_1(x_1,y_1)$ and $P_2(x_2,y_2)$ is defined as

\|P_1P_2\|=|x_1-x_2|+|y_1-y_2|.

Let $F_1$ , $F_2$ be two distinct fixed points on the $x$ -axis. Describe the shape of the locus of points whose sum of L-distances to $F_1$ and $F_2$ equals a fixed constant greater than $\|F_1F_2\|$ .

Answer

Solution

Difficulty	7/10
Topics	Absolute Value, analytic geometry, Casework

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