0
A parabola is the set of all points that A are the same distance from a point and a line B are the same distance from one point C are the same distance from two points?
Wiki User
∙ 13y ago
Alternates are fill-in-the-blank version of this Q.
are the same distance from a point and a line
Wiki User
∙ 13y ago
Add your answer:
Earn +20 pts
What is the definition of parabola?
There are several ways of defining a parabola. Here are some:Given a straight line and a point not on that line, a parabola is the locus of all points that are equidistant from that point (the focus) and the line (directrix).A parabola is the intersection of the surface of a right circular cone and a plane parallel to a generating line of that surface.A parabola is the graph of a quadratic equation.
How many foci does a parabola have?
A parabola has a single focus point. There is a line running perpendicular to the axis of symmetry of the parabola called the directrix. A line running from the focus to a point on the parabola is going to have the same distance as from the point on the parabola to the closest point of the directrix. In theory you could look at a parabola as being an ellipse with one focus at infinity, but that really doesn't help any. ■
Which geometric object is defined as the set of all points in a plane that are equidistant from a point and a line?
parabola
What is the shortest distance between four points?
The shortest distance between four points is a straight line to and from each individual point. If all four points are aligned, the result will be a single straight line through all four points.
Can a ray be a line segment?
No. A ray is infinite on one side and ends at a point at the other. A line segment ends in two points. A ray can contain a line segment, as the distance between any two given points on the ray is a line segment.
The locus of points which are are the same distance from a point and a line is called a?
parabola
Which best describes a parabola?
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.
What does parabola mean in mathematical terms?
It is the locus of all points such that their distance from a fixed line (the directrix) is the same as their distance from a fixed point which is not on that line (the focus).
Are the directrix and focus different distances from a given point on a parabola?
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).
What is the directrix of a parabola?
"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
What is the definition of parabola?
There are several ways of defining a parabola. Here are some:Given a straight line and a point not on that line, a parabola is the locus of all points that are equidistant from that point (the focus) and the line (directrix).A parabola is the intersection of the surface of a right circular cone and a plane parallel to a generating line of that surface.A parabola is the graph of a quadratic equation.
How many foci does a parabola have?
A parabola has a single focus point. There is a line running perpendicular to the axis of symmetry of the parabola called the directrix. A line running from the focus to a point on the parabola is going to have the same distance as from the point on the parabola to the closest point of the directrix. In theory you could look at a parabola as being an ellipse with one focus at infinity, but that really doesn't help any. ■
Which geometric object is defined as the set of all points in a plane that are equidistant from a point and a line?
parabola
How do you best describe a parabola?
The set of all points in a plane that are equidistant from a single point and a single line
What conic section is defined by the set of all points in a plane that are equidistant from a single point and a line?
It is a parabola.
How do the characteristics and equations of a circle differ from those of a parabola?
In its standard form, the equation of a circle is a quadratic in both variables, x and y, whereas a parabola is quadratic in one (x) and liner in the other (y). A circle is a closed shape and comprises the locus of all points that are equidistant from one given point (the centre). A parabola is an open shape and comprises the locus of all points that are the same distance from a a straight line (the directrix) and a point not on that line (the focus).
What is a point equal distance from the end points of a line?
The point that is equal distance from the endpoints of a line segment is the midpoint.
