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Directrix is a spaceship in the Lensman series of novels by E. E. Smith. Directrix is the name of an alternative punk band in Chicago. Directrix - a feminine form of director in the context of grammatical gender
The ellipse thus generated has its second focus at the center of the directrix circle, and the ellipse lies entirely within the circle. For the parabola, the center of the directrix moves to the point at infinity (see Projective geometry). The directrix "circle" becomes a curve with zero curvature, indistinguishable from a straight line.
(1) All rulings are parallel to a plane, the directrix plane. (2) All rulings intersect a fixed line, the axis. The conoid is a right conoid if its axis is perpendicular to its directrix plane. Hence all rulings are perpendicular to the axis. Because of (1) any conoid is a Catalan surface and can be represented parametrically by
A family of conic sections of varying eccentricity share a focus point and directrix line, including an ellipse (red, e = 1/2), a parabola (green, e = 1), and a hyperbola (blue, e = 2). The conic of eccentricity 0 in this figure is an infinitesimal circle centered at the focus, and the conic of eccentricity ∞ is an infinitesimally separated ...
Ruled surface generated by two Bézier curves as directrices (red, green). A surface in 3-dimensional Euclidean space is called a ruled surface if it is the union of a differentiable one-parameter family of lines.
The directrix is the perpendicular to line ¯ through point . Alternative construction of E 1 {\displaystyle E_{1}} : Calculation shows, that point E 1 {\displaystyle E_{1}} is the intersection of the asymptote with its perpendicular through F 1 {\displaystyle F_{1}} (see diagram).
In this diagram, F is the focus of the parabola, and T and U lie on its directrix. P is an arbitrary point on the parabola. PT is perpendicular to the directrix, and the line MP bisects angle ∠FPT. Q is another point on the parabola, with QU perpendicular to the directrix. We know that FP = PT and FQ = QU.
Neither Dandelin nor Quetelet used the Dandelin spheres to prove the focus-directrix property. The first to do so may have been Pierce Morton in 1829, [8] or perhaps Hugh Hamilton who remarked (in 1758) that a sphere touches the cone at a circle which defines a plane whose intersection with the plane of the conic section is a directrix.