Locus of Intersection of Tangents at the End of Conjugate Diameters

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We create a tangent, then a line HL through the center of the ellipse parallel to the tangent. We then intersect the original tangent with the tangent at this new point L. The locus is seen to be an ellipse.

Show that the new ellipse is a dilation of the old ellipse by a factor of sqrt(2).

Expressions

Name Input
Locus Derive Input Maple Input MathML Input Mathematica Input Maxima Input Mupad Input TI-Nspire Input text Input Image
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