Question

a parabola is the set of all points that:
a. are the same distance from two points.
b. are the same distance from one point.
c. are the same distance from two lines.
d. are the same distance from a point and a line.

Explanation:

Step1: Recall the definition of a parabola

A parabola is defined as the set of all points in a plane that are equidistant from a fixed point (called the focus) and a fixed line (called the directrix).

Step2: Analyze each option

• Option A: The set of points equidistant from two points is a perpendicular bisector of the segment joining the two points, not a parabola.
• Option B: The set of points equidistant from one point is a circle (if in 2 - D, the set of points at a fixed distance from a center point).
• Option C: The set of points equidistant from two lines (depending on the lines, if parallel, it is a line midway between them; if intersecting, it is a pair of angle - bisecting lines), not a parabola.
• Option D: This matches the definition of a parabola (equidistant from a point (focus) and a line (directrix)).

Answer:

D. are the same distance from a point and a line.