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The distance between the vertex and the focus, measured along the axis of symmetry, is the "focal length". The "latus rectum" is the chord of the parabola that is parallel to the directrix and passes through the focus. Parabolas can open up, down, left, right, or in some other arbitrary direction.
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.
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.
A family of conic sections of varying eccentricity share a focus point F and directrix line L, 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 ...
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 ...
In mathematics, a directrix is a curve associated with a process generating a geometric object, such as: Directrix (conic section) Directrix (ellipse) Directrix ...
A parabola, showing directrix (L) and focus (F). Generic points marked for explanation. File usage. The following page uses this file: File:Parabola with focus and ...
by using a translation of axes, determine whether the locus of the equation is a parabola, ellipse, or hyperbola. Determine foci (or focus), vertices (or vertex), and eccentricity . Solution: To complete the square in x and y , write the equation in the form