Lemma
MediumConic sections
OpenStax, Algebra and Trigonometry 2e §12.5 Conic Sections in Polar Coordinates · Review Exercise 81 · Geometry · Conic sections

Conic Sections in Polar Coordinates · Review Exercise 81

Find the equation of the hyperbola.

Foci at and vertex at

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OpenStax, Algebra and Trigonometry 2e · §12.5 Conic Sections in Polar Coordinates · Review Exercise 81

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Checked against the answer in OpenStax, Algebra and Trigonometry 2e.