Ellipse and the Right Angle

Geometry Level 4

Below is the graph of the ellipse x216+y29=1\large\frac{x^2}{16}+\frac{y^2}{9}=1 and two lines that are tangent to the ellipse and meet at right angles at a point P.P. If we trace out the path of P,P, its total length can be expressed as kπ.k\pi. What is k?k?

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