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Chapter 6: Problem 1

The locus of a point in the plane that moves such that its distance from a fixed point (focus) is in a constant ratio to its distance from a fixed line (directrix) is a _____.

Short Answer

Expert verified
The locus of the point is a parabola.

Step by step solution

01

Parse the Problem Statement

Begin by understanding the elements mentioned in the problem. There's a point that moves in such a way that its distance from a fixed point - called the focus - is always proportionate to its distance from a fixed line - the directrix.
02

Connect Problem Statement to Known Definitions

Reflect on the definitions and properties of conic sections. In a conic section, a point moves such that its distance from a fixed point (the focus) bears a constant ratio to its perpendicular distance from a fixed line (the directrix). This is the defining property of a certain type of conic section.
03

Identify the Conic Section

The conic section in the problem statement is a parabola. In a parabola, the ratio of the distance of a point from the focus to its distance from the directrix is always equal to one, and this ratio is consistent for all points on the parabola.

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