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Q: The set of all points equidistant from a point called the focus and a line called the directrix?

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true

Because that is how a parabola is defined!

A form of arch defined by a moving point which remains equidistant from a fixed point inside the arch and a moving point along a line. This shape when inverted into an arch structure results in a form which allows equal vertical loading along its length. A parabola is the graph of a quadratic equation. Mathworld has some nice drawings. Need a link? You got it. A Parabola is the set of all points that are equidistant from a point and a line. The line is called the directrix and the point is called the focus. Each point on the parabola is as far from the directrix as it is from the focus. It is the same shape of a curve you will find in the reflector of a flashlight bulb, or in the arc of a baseball when it is thrown or hit.

A parabola.

parabola

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the set of points equidistant from a fixed point

Because that is how a parabola is defined!

from any point and the dirextix

One definition of a parabola is the set of points that are equidistant from a given line called the directrix and a given point called the focus. So, no. The distances are not different, they are the same. The distance between the directrix and a given point on the parabola will always be the same as the distance between that same point on the parabola and the focus. Any point where those two distances are equal would be on the parabola somewhere and all the points where those two distances are different would not be on the parabola. Note that the distance from a point to the directrix is definied as the perpendicular distance (also known as the minimum distance).

FALSE. One of the definitions of a parabola, and also a means of drawing it, is that EVERY point on it is equidistant from the focus and the directrix.

"From the geometric point of view, the given point is the focus of the parabola and the given line is its directrix. It can be shown that the line of symmetry of the parabola is the line perpendicular to the directrix through the focus. The vertex of the parabola is the point of the parabola that is closest to both the focus and directrix."-http://www.personal.kent.edu/~rmuhamma/Algorithms/MyAlgorithms/parabola.htm"A line perpendicular to the axis of symmetry used in the definition of a parabola. A parabola is defined as follows: For a given point, called the focus, and a given line not through the focus, called the directrix, a parabola is the locus, or set of points, such that the distance to the focus equals the distance to the directrix."-http://www.mathwords.com/d/directrix_parabola.htm

Given a straight line (a directrix) and a point (the focus) which is not on that line, a parabola is locus of all points whose distance form the directrix is the same as its distance from the focus.

A form of arch defined by a moving point which remains equidistant from a fixed point inside the arch and a moving point along a line. This shape when inverted into an arch structure results in a form which allows equal vertical loading along its length. A parabola is the graph of a quadratic equation. Mathworld has some nice drawings. Need a link? You got it. A Parabola is the set of all points that are equidistant from a point and a line. The line is called the directrix and the point is called the focus. Each point on the parabola is as far from the directrix as it is from the focus. It is the same shape of a curve you will find in the reflector of a flashlight bulb, or in the arc of a baseball when it is thrown or hit.

It is the vertex of the parabola.

parabola

A parabola.