Recall Properties Of Ellipse

Calculus Level 5

Let the equation of an ellipse be x2a2+y2b2=1.\frac { { x }^{ 2 } }{ { a }^{ 2 } } +\frac { { y }^{ 2 } }{ { b }^{ 2 } } =1. Now, a point P=(α,β)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 P1P_1 and P2P_2, respectively.

If b=3,b=3, what is the absolute value of (P1P2)?(P_1-P_2) ?

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