# Cutting The Paraboloid

Geometry Level 5

A paraboloid is given by $$z = x^2 + \dfrac{1}{4} y^2$$.

A plane whose equation is $$x + y + 2 z = 2$$ cuts through it. The resulting intersection is an ellipse. Find the sum of the semi-minor and semi-major axes of the ellipse. Round your answer to three decimal places.

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