# Ellipse and the Right Angle

Geometry Level 4

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

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