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A line through the focus and a line perpendicular to the directrix make the same angle with the tangent.
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Given a point (the focus) and a line (the directrix), a parabola can be defined as the locus of the points whose distance from the focus is equal to t...
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We take the parabola, whose vertex is (0,0) and whose focus is (0,a). The point at parametric location t is (2*a*t,a*t^2).
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Take two tangents of a parabola that are perpendicular to each other. The locus of all such points will be a line. This line is the directrix.
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The slope of the tangent at parametric location t gives a further characterization:
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This is the directrix.
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Take two nonparallel tangents of a parabola, and the angle at their intersection can be calculated.
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We look at the caustic of the parabola y=x^2 formed by a set of rays at angle θ to the x-axis.
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