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If we intersect the tangent at parametric location t with the axes, we observe that each intersection is independent of one of the parameters of the e...
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Take two tangents of an ellipse that are perpendicular to each other. The locus of all such points will be a circle.
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Salmon calls this the “Eccentric angle”. For an ellipse, the point at parametric location t is the point
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Take two nonparallel tangents of an ellipse, and the angle at their intersection can be calculated.
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Expressed in terms of slopes we see that the product of the slopes of the diameter and its tangent is -b^2/a^2.
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Position the end of a diameter at parametric location t. Find the angle between the chords to a point at parametric location s.
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We look at the locus of the intersections of the tangents at the end of the diameter and the focal chord through a point. This locus is a circle with ...
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We examine lines through the foci perpendicular to the tangent at a point. Take the diagonals of the trapezoid formed by the tangent, the two perpendi...
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