A Conic Through Four Intersections

★ 7/10conic sections analytic geometry Symmetry

Problem

Find the equation of the conic that passes through all intersection points of

F: x^2 + 2y^2 - 2 = 0 \qquad\text{and}\qquad G: 2x^2 - y^2 - 2 = 0,

and whose chord cut by the $y$ -axis has length $\sqrt{13}$ .

Answer

Solution

Difficulty	7/10
Topics	conic sections, analytic geometry, Symmetry

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