###### Asked in Geometry

Geometry

# Is equidistant from a given directrix and focus?

## Answer

###### Wiki User

###### June 22, 2017 5:57PM

Any point on a parabola.

## Related Questions

###### Asked in Algebra, Geometry

### 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

###### Asked in Math and Arithmetic, Algebra, Geometry

### 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).

###### Asked in Geometry

### Which best describes a parabola?

###### Asked in English Language, Math and Arithmetic, Definitions

### 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.

###### Asked in Calculus

### What are the steps solving a parabola?

The answer will depend on
what you mean by "solving a parabola". A parabola has a
directrix and a focus, a turning point, 0 1 or 2 roots and so on.
Which of these is "solving"?
The answer will depend on
what you mean by "solving a parabola". A parabola has a
directrix and a focus, a turning point, 0 1 or 2 roots and so on.
Which of these is "solving"?
The answer will depend on
what you mean by "solving a parabola". A parabola has a
directrix and a focus, a turning point, 0 1 or 2 roots and so on.
Which of these is "solving"?
The answer will depend on
what you mean by "solving a parabola". A parabola has a
directrix and a focus, a turning point, 0 1 or 2 roots and so on.
Which of these is "solving"?

###### Asked in School Subjects, Math and Arithmetic, Algebra, Geometry

### What is a parabola?

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.

###### Asked in Math and Arithmetic, Algebra, Geometry

### 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. ■

###### Asked in Math and Arithmetic, Algebra, Geometry

### 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).

###### Asked in Math and Arithmetic, Algebra

### How would you find the vertex p value focus directrix and focal width of negative one fourth x squared equals y?

-(1/4) x2 = y . . . putting this in the standard form x2 = 4cy
it becomes :
x2 = 4*(-1)y = -4y.
This tells us that the parabola is a downward opening parabola
with its vertex at the origin(0.0).
The focus is at a distance of -1 from the vertex, that is
(0,-1).
The directrix is equidistant to the focus but on the opposite
side of the vertex and is thus the line y = 1.
The length of the chord passing through the focus and
perpendicular to the major axis is called the Latus Rectum and has
a length of 4c. As c = -1 then the length is 4 but again shows as a
negative value as it is "below" the vertex.

###### Asked in Math and Arithmetic, Algebra, Calculus

### What does 4 stands for in equation of parabola square of square of y equals 4ax?

A parabola with an equation, y2 = 4ax has its vertex at the
origin and opens to the right.
It's not just the '4' that is important, it's '4a' that
matters.
This type of parabola has a directrix at x = -a, and a focus at
(a, 0). By writing the equation as it is, the position of the
directrix and focus are readily identifiable.
For example, y2 = 2.4x doesn't say a great deal. Re-writing the
equation of the parabola as y2 = 4*(0.6)x tells us immediately that
the directrix is at x = -0.6 and the focus is at (0.6, 0)

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