Assertion: parabola's point | /r/HasProperty | equidistant
Facets:
value: from the directrix
type: OTHER
value: from the focus
type: OTHER
value: from a given point
type: OTHER
value: from a line
type: OTHER
value: from f
type: OTHER
value: from (o, p)
type: OTHER
value: from line d
type: LOCATION
value: because of the definition of a parabola
type: CAUSE
value: from a certain point
type: TEMPORAL
value: from the end points
type: LOCATION
value: from t
type: LOCATION
Source sentences:
text: In the following proof, the fact that every point on the parabola is equidistant from the focus and from the directrix is taken as axiomatic.
text: The parabolic curve itself is the set of all points that are equidistant (equal distances) from both the directrix line and the focus.
text: All points on the bisector MP are equidistant from F and T, but Q is closer to F than to T.
text: The parabola is the curve formed from all the points (x, y) that are equidistant from the directrix and the focus .
text: A parabola can also be defined as locus of points which are equidistant from a given point (the focus) and a given line (the directrix).
text: A Parabola is the set of all points that are equidistant from a point and a line.
text: Every point on a parabola is equidistant from a certain point and a line.
text: The locus of points in that plane that are equidistant from both the directrix and the focus is the parabola.
text: A Parabola, as a locus of points , is the set of all points that are equidistant from a point and a line.
text: We must show that a point (x, y) that is equidistant from (o, p) and the line y = -p also satisfies the equation y = 1/4p x2
text: The parabola is constructed of infinitely many points that are equidistant from the focus and the directrix.
text: We use the fact that his point must be equidistant from F and line D, such that the distance formula from F to P must be the same as P to D.
text: We use the fact that his point must be equidistant from F and line D, such that the distance formula from F to P must be the same as P to D.
text: As the parabola is a locus of all the points which are equidistant from the focus and the directrix, its ration will always be 1 that is, e = 1
text: A parabola can also be defined as locus of points which are equidistant from a given point (the focus) and a given line (the directrix).
text: Definition: The locus of all points that are equidistant from a given point (focus)and a given line (directrix).
text: We know by definition that any point P(x,y) on the parabola is equidistant from the focus and directrix.
text: Sketch the curve of the parabola by making sure the points on the curve are equidistant from the focus and directrix.
text: We cannot call any U-shaped curve as a parabola; it is essential that every point on this curve be equidistant from the focus and directrix.
text: Now we know that any point on the perpendicular bisector of segment AF is equidistant from the end points.
text: If you take a straight line, which is called the directrix, and some point not on the line, which is called the focus, then a parabola is the locus of the points that are equidistant from the focus and the directrix.
text: A parabola, shown in Figure 1, below, is a special mathematical shape — a curve consisting of the points that are equidistant from both a given fixed point called the focal point or (focus) and a given fixed line (called the directrix).
text: Every point on a parabola (curved red line) is equidistant from both a given point called the focal point and a given line called the directrix.
text: Every point on a parabola (curved red line) is equidistant from both a given point called theand a given line called the.
text: Of course, as I mentioned before, this point must be equidistant from the focus and from the directrix because of the definition of a parabola.