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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).
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.
The directrix and focus are the same distance from a given point on the parabola?
true
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?
9
Is equidistant from a given directrix and focus?
Any point on a parabola.
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 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.
The vertex is the extreme point of a parabola and is located halfway between the and directrix?
focus
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
The is the extreme point of a parabola and is located halfway between the focus and directrix.?
This extreme point on the parabola is called the vertex. In math. a parabola is a U-shaped curve with a directrix, which is a fixed straight line.
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
How do you find a p value when given the focus and directrix?
To find the p-value for a parabola given its focus and directrix, first identify the coordinates of the focus (F) and the equation of the directrix (a line). The p-value represents the distance from the vertex of the parabola to the focus (or the vertex to the directrix), which is half the distance between them. Calculate this distance using the formula for distance between a point and a line, or by measuring the distance from the vertex to either the focus or the directrix. The p-value is then the absolute value of this distance.
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.
