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the set of points equidistant from a fixed point
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What is the extreme point of a parabola that is located halfway between the focus and directrix called?
It is the vertex of the parabola.
The directrix and focus are different distances from a given point on the parabola. A. True B. False?
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.
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. ■
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.
What is the equation of the quadratic graph with a focus of (3 6) and a directrix of y 4?
For a parabola with a y=... directrix, it is of the form: (x - h)^2 = 4p(y - k) with vertex (h, k), focus (h, k + p) and directrix y = k - p With a focus of (3, 6) and a directrix of y = 4, this means: (h, k + p) = (3, 6) → k + p = 6 y = k - p = 4 → k = 5, p = 1 (solving the simultaneous equations) → vertex is (3, 5) → parabola is (x - 3)^2 = 4(y - 5) which can be rearranged into y = 1/4 x^2 - 3/2 x + 29/4
What is the midpoint of the parabola between the focus and the directrix?
It is the apex of the parabola.
Is it true or false that the directrix and focus are different distances from a given point on a parabola?
True. In a parabola, any point on the curve is equidistant from the focus and the directrix. This means that while the distances to the focus and directrix are equal for points on the parabola, they are different distances from any point not on the parabola.
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 geometric shape has focus and directrix?
A parabola.
What object using a directrix and a focus?
parabola
If the distance from the green point on the parabola to the parabola's focus is 7 What is the distance from the green point to the directrix?
In a parabola, the distance from any point on the curve to the focus is equal to the distance from that point to the directrix. If the distance from the green point on the parabola to the focus is 7, then the distance from the green point to the directrix is also 7. Therefore, the distance from the green point to the directrix is 7.
Why is every point on a parabola equidistant to the focus and the directrix?
Because that is how a parabola is defined!
What object is defined using a directrix and a focus?
parabola
The distance from the green point on the parabola to the parabola's focus is 9. What is the distance from the green point to the directrix?
In a parabola, the distance from any point on the parabola to the focus is equal to the distance from that point to the directrix. Since the distance from the green point on the parabola to the focus is given as 9, the distance from the green point to the directrix is also 9. Thus, both distances are equal.
What are the steps solving a parabola?
The answer will depend onwhat 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 onwhat 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 onwhat 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 onwhat 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 is the extreme point of a parabola and is located halfway between the focus and directrix?
The vertex -- the closest point on the parabola to the directrix.
What is Focus (34) directrix y -2?
The focus of a parabola is a specific point that defines its shape, while the directrix is a line used in the definition of a parabola. If the directrix is given as ( y = -2 ), the parabola opens either upwards or downwards. The focus would be located at a point above or below this directrix, depending on the orientation of the parabola. Specifically, for a parabola that opens upwards, the focus would be positioned at ( (h, k + p) ), where ( p ) is the distance from the vertex to the focus, and the vertex would be located at ( (h, -2 + p) ).
