What is the textbook definition of the focus of a parabola?

Answer 1

If you start with a line and a point not on that line, then determine the set of points which are equidistant from the line and the point, this set of points is called:

"the parabola" determined by the line and the point

the line is called "the directrix" (of "the parabola")

the point is called "the focus" (of "the parabola")

Answer 2

A parabola is defined as the locus of all points in a plane that are equidistant forom a line called the directrix and a point (not on the given line) called the focus.

The line through the focus and perpendicular to the directrix is called the axis of symmetry of the parabola.The point on the axis halfway between the focus and the drectrix is called the vertex of the parabola.

Answer 3

Focus is actually part of the definition of a parabola: A parabola is defined as the locus of all points which are equidistant to a given point and a given line. The given point is called the focus, and the given line the directrix. And that's the textbook definition!

Answer 4

There is more than one text book definition. Here is one of them.

Pick a line "l" and a point "f" not on the line. Now, find all of the points (x,y) such that the distance from f to (x,y) is equal to the distance from (x,y) to the line. That collection of point is a parabola and the point "f" is the focus.

HTH

Charles