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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
