Ellipses

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We look at the locus of the projection of the center onto a tangent. The locus has this more suggestive equation: (X^2+Y^2)^2=(aX)^2+(bY)^2.
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The latus rectum is the chord through the focus to the ellipse perpendicular to the major axis. We look at the length of the semi latus rectum.
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The locus of the vertex of this triangle is the following 4th order curve:
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Take a chord in an ellipse and the tangent at one end. Then, take a line parallel to the chord from the center to the tangent. The locus of the inters...
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This is the directrix:
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Draw a line from the center of the ellipse to the tangent, parallel to the focal radius (line from the focus to the point of tangency). We see this h...
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The distance of any point on the conic from the focus is equal to the whole length of the ordinate at that point, produced to meet the tangent at the ...
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If a quadrilateral circumscribes a central conic, the line joining the centers of its diagonals passes through the center of the conic.
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