Slicing a Cone at $45^\circ$

★ 7/10solid geometry Completing the Square conic sections Solids of Revolution analytic geometry

Problem

A conical surface has apex $S$ , and its generators make an angle of $30^\circ$ with the axis. A point $C$ on the axis satisfies $SC = 5$ . A plane through $C$ making an angle of $45^\circ$ with the axis cuts the cone. Prove that the section is an ellipse, and find its equation in suitable rectangular coordinates in the cutting plane (centered at the ellipse's center).

Answer

Solution

Difficulty	7/10
Topics	solid geometry, Completing the Square, conic sections, Solids of Revolution, analytic geometry

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