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 (PF)(PF)d 2 is constant as P varies on the ellipse, where PF 1 and PF 2 are the distances from P to the foci F 1 and F of the ellipse

Question: 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

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 (PF₁)(PF₂)d² is constant as P varies on the ellipse, where PF₁ and PF₂ are the distances from P to the foci F₁and F₂ of the ellipse.

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