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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.
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).
Is equidistant from a given directrix and focus?
Any point on a parabola.
The directrix and focus are different distances from a given point on the parabola?
false
What is the equation of a parabola with vertex at 1 -3 and focus at 2 -3?
For a parabola with an axis of symmetry parallel to the x-axis, the equation of a parabola is given by: (y - k)² = 4p(x - h) Where the vertex is at (h, k), and the distance between the focus and the vertex is p (which can be calculated as p = x_focus - x_vertex). For the parabola with vertex (1, -3) and focus (2, -3) this gives: h = 1 k = -3 p = 2 - 1 = 1 → parabola is: (y - -3)² = 4×1(x - 1) → (y + 3)² = 4(x - 1) This can be expanded to: 4x = y² + 6y + 13 or x = (1/4)y² + (3/2)y + (13/4)
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 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
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.
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).
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.
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) ).
A parabola is defined as all points equidistant from a given directrix and focus.?
true
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.
Is equidistant from a given directrix and focus?
Any point on a parabola.
How do you get directrix of a parabola?
The directrix of a parabola can be found using its standard form equation. For a parabola that opens upwards or downwards, given by (y = ax^2 + bx + c), the directrix is located at (y = k - \frac{1}{4p}), where (k) is the vertex's y-coordinate and (p) is the distance from the vertex to the focus. For a parabola that opens sideways, the directrix is given by (x = h - \frac{1}{4p}), where (h) is the vertex's x-coordinate. The value of (p) can be determined based on the coefficients of the quadratic equation.
The directrix and focus are different distances from a given point on the parabola?
false
What is the equation of a parabola with vertex (0 0) and directrix x -3.?
The equation of a parabola with vertex at (0, 0) and a directrix of ( x = -3 ) opens to the right, as the directrix is a vertical line. The distance from the vertex to the directrix is 3 units. The standard form of the equation for a horizontally-opening parabola is given by ( y^2 = 4px ), where ( p ) is the distance from the vertex to the directrix. Therefore, with ( p = 3 ), the equation is ( y^2 = 12x ).
