Search results
Results from the WOW.Com Content Network
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 ...
A consequence is that the equation (in ,) of the parabola determined by 3 points = (,), =,,, with different x coordinates is (if two x coordinates are equal, there is no parabola with directrix parallel to the x axis, which passes through the points) =.
Conic sections of varying eccentricity sharing 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 pair of lines.
It has been proved that the Kiepert hyperbola is the hyperbola passing through the vertices, the centroid and the orthocenter of the reference triangle and the Kiepert parabola is the parabola inscribed in the reference triangle having the Euler line as directrix and the triangle center X 110 as focus. [1]
The same set of points can often be constructed using a smaller set of tools. For example, using a compass, straightedge, and a piece of paper on which we have the parabola y=x 2 together with the points (0,0) and (1,0), one can construct any complex number that has a solid construction. Likewise, a tool that can draw any ellipse with already ...
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.
An illustration of various conic constants. In geometry, the conic constant (or Schwarzschild constant, [1] after Karl Schwarzschild) is a quantity describing conic sections, and is represented by the letter K.
In mathematics, a directrix is a curve associated with a process generating a geometric object, such as: Directrix (conic section) Directrix (generatrix)