Recall Properties Of Ellipse

Calculus Level 5

Let the equation of an ellipse be \[\frac { { x }^{ 2 } }{ { a }^{ 2 } } +\frac { { y }^{ 2 } }{ { b }^{ 2 } } =1.\] Now, a point \(P=(\alpha ,\beta )\) lies on the ellipse and a tangent is drawn to the ellipse at that point.

The perpendicular distance from the origin to this tangent is 5, and the perpendicular distances from the foci to the tangent are \(P_1\) and \(P_2\), respectively.

If \(b=3,\) what is the absolute value of \((P_1-P_2) ?\)

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