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An Elliptic Identity

​
semi-major axis a
1.7
semi-minor axis b
1.1
EF × EG ×
2
OP
=3.5
2
a
2
b
=3.5
Let E be a point on an ellipse, O its center, F and G its two foci, and P the point on the tangent line to E such that OP is perpendicular to the tangent line. Then the identity is
EF×EG
×
2
OP
=
2
a
2
b
. Drag the point E to see that the identity holds for ellipses of different shapes and sizes.
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