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Tangents to a conic

Author:
Darryl Yong
F1 and F2 are foci for a conic section. You can produce both ellipses and hyperbolas. The orange lines are tangents to the conic passing through X. Can you figure out how the construction works? Link to download this GeoGebra file: http://tube.geogebra.org/material/download/format/file/id/1415145

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