Vault Of Euclid

Equation of an Ellipse from Vertices and Foci

Parametric equations and vector functions core

Endpoints of major axis at \((-3, 5)\), \((-3, -3)\) and foci located at \((-3, 3)\), \((-3, -1)\)
ellipseconic-sectionsanalytic-geometrymajor-axisfociverticescenterstandard-equationfind-equationprecalculusalgebra

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What this problem tests

Tests the ability to identify the orientation of an ellipse, find its center using the midpoint formula, and use the relationship between a, b, and c to complete the standard equation.

This is a standard exercise in precalculus and analytic geometry, testing the student's ability to construct the equation of a conic section from its geometric properties.

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