Constant Product of Slopes: Ellipse and Hyperbola Property
2021-01-10 14:22
This GeoGebra example demonstrates a fundamental property in coordinate geometry: when a point P moves along an ellipse or hyperbola, the product of the slopes of lines connecting P to two specific points (such as endpoints of a diameter or symmetric points) remains constant. For an ellipse x²/a²+y²/b²=1, this constant equals -b²/a²; for a hyperbola, it equals b²/a². The construction uses points,
In collections
Conic Sections - Interactive GeoGebra Book
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