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A parabola is defined as all points equidistant from a given directrix and focus.?
true
Locus of points that sre the same distance from a point and a line is a?
The locus of points that are the same distance from a point and a line is a parabola. The fixed point is called the focus of the parabola, while the line is referred to as the directrix. Each point on the parabola is equidistant from the focus and the directrix, which defines its shape and properties.
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.
The locus of points that are the same distance from a point and a line is a .?
The locus of points that are the same distance from a point and a line is a parabola. In this scenario, the point acts as the focus of the parabola, while the line serves as the directrix. The shape of the parabola opens away from the line, with all points on the curve equidistant from both the focus and the directrix.
Why is every point on a parabola equidistant to the focus and the directrix?
Because that is how a parabola is defined!
A parabola is defined as all points equidistant from a given directrix and focus.?
true
Briefly explain the focus and directrix of a parabola?
the set of points equidistant from a fixed point
Locus of points that sre the same distance from a point and a line is a?
The locus of points that are the same distance from a point and a line is a parabola. The fixed point is called the focus of the parabola, while the line is referred to as the directrix. Each point on the parabola is equidistant from the focus and the directrix, which defines its shape and properties.
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.
The locus of points that are the same distance from a point and a line is a .?
The locus of points that are the same distance from a point and a line is a parabola. In this scenario, the point acts as the focus of the parabola, while the line serves as the directrix. The shape of the parabola opens away from the line, with all points on the curve equidistant from both the focus and the directrix.
Why is every point on a parabola equidistant to the focus and the directrix?
Because that is how a parabola is defined!
Is equidistant from a given directrix and focus?
Any point on a parabola.
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).
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.
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
How does one create a parabola?
A parabola can be created by plotting points that satisfy the quadratic equation of the form (y = ax^2 + bx + c), where (a), (b), and (c) are constants. Alternatively, it can be formed geometrically by taking a fixed point (the focus) and a fixed line (the directrix); the set of all points equidistant from both the focus and the directrix defines the parabola. To visualize it, you can also use graphing software or tools to draw it based on these principles.
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.
