Ellipses

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An ellipse can be defined as the locus of points, the sum of whose distances to two fixed points (the foci) is constant. This is the elementary “two ...
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With given semi-major axes and semi-minor axes, we can define two foci, and therefore an ellipse, that will satisfy those axes.
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The foci have the property that the lines from the foci to a point on the curve make equal angles to the tangent. Hence, light shone from one focus r...
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The subnormal to point C on the curve is the segment from the intersection of the normal at C with the major axis, to the foot of the perpendicular dr...
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Given a point (the focus) and a line (the directrix), we examine the locus of the points whose distance from the focus is k times the distance from th...
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Where does the normal intersect the major axis?
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Given a point D in an ellipse, draw a chord through D. Find the intersection of the the tangents at the end of the chord. The locus of all such inters...
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A pair of diameters is conjugate if each is parallel to the tangents at the ends of the other. We show that the diameters of points whose parameters ...
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