Find the standard equation of an ellipse given the coordinates of its foci and its eccentricity.

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Equation of an Ellipse from Foci and Eccentricity

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Find the equation of the conic section with foci located at \( (2, 0) \) and \( (-2, 0) \) and an eccentricity of \( \frac{1}{2} \).

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What you need first

Definition of eccentricity
Standard forms of conic sections
Relationship between a, b, and c in an ellipse

What this problem tests

Tests the ability to identify a conic section from its eccentricity and to use the relationships between a, b, c, and e to construct its standard equation.

This is a standard exercise in precalculus and analytic geometry, often used to introduce the algebraic properties of conic sections.

Equation of an Ellipse from Foci and Eccentricity

What you need first

What this problem tests

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