# A planar cut through an Elliptical Cylinder

Geometry Level 5

$\large \dfrac{x^2}{100} + \dfrac{y^2}{225} = 1$

A right cylinder whose axis is along the $$z$$-axis, has an elliptical cross-section (in the horizontal plane) given above.

If a plane whose equation is $$\sqrt{2} x + \sqrt{2} y + 2 \sqrt{3} z = 100 \sqrt{3}$$, cuts through the cylinder, then the cutting plane and the cylinder intersect in an ellipse. Find the sum of the semi-minor and semi-major axes of this ellipse.

Round your answer to three decimal places.

×