For a point P on an ellipse, let d be the distance from the center of the ellipse to the line tangent to the ellipse at P . Prove that ( P F 1 ) ( P F 2 ) d 2 is constant as P varies on the ellipse, where P F 1 and P F 2 are the distances from P to the foci F 1 and F 2 of the ellipse.
For a point P on an ellipse, let d be the distance from the center of the ellipse to the line tangent to the ellipse at P . Prove that ( P F 1 ) ( P F 2 ) d 2 is constant as P varies on the ellipse, where P F 1 and P F 2 are the distances from P to the foci F 1 and F 2 of the ellipse.
Solution Summary: The author explains how the expression (PF_1)d2 is constant as P varies on the ellipse.
For a point P on an ellipse, let d be the distance from the center of the ellipse to the line tangent to
the ellipse at P. Prove that
(
P
F
1
)
(
P
F
2
)
d
2
is constant as P varies on the ellipse, where
P
F
1
and
P
F
2
are the distances from P to the foci
F
1
and
F
2
of the ellipse.
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