Find the equation of a hyperbola given the endpoints of its conjugate axis and the locations of its foci.

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Equation of a Hyperbola from Foci and Conjugate Axis

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Endpoints of the conjugate axis located at \( (0, 3), (0, -3) \) and foci located \( (4, 0), (-4, 0) \).

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What you need first

the geometric definition and standard forms of a hyperbola
the relationship between the transverse axis, conjugate axis, and foci of a hyperbola

What this problem tests

Tests the ability to identify the orientation of a hyperbola from given points and to use the relationship c^2 = a^2 + b^2 to find missing parameters.

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

Equation of a Hyperbola from Foci and Conjugate Axis

What you need first

What this problem tests

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