Hyperbolas Review

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What is a hyperbola?

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A hyperbola is a type of conic section that appears as two separate curves, defined as the set of all points where the difference of the distances to two fixed points (foci) is constant.

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What is the standard form of a hyperbola centered at (h, k) with a vertical transverse axis?

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What is the standard form of a hyperbola centered at (h, k) with a horizontal transverse axis?

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How do you find the vertices of a hyperbola?

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The vertices are located at a distance 'a' from the center along the transverse axis. For a vertical hyperbola, they are at (h, k±a); for a horizontal hyperbola, at (h±a, k).

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What is the relationship between the foci and the vertices of a hyperbola?

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What are the asymptotes of a hyperbola?

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The asymptotes are lines that the hyperbola approaches but never touches. For a hyperbola centered at (h, k), the equations are: y = k ± (a/b)(x-h) for a vertical hyperbola and y = k ± (b/a)(x-h) for a horizontal hyperbola.

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The center is (0, -3).

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The vertices are (2, 1) and (2, -4).

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What is the distance between the foci of a hyperbola?

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The distance between the foci is 2c, where c is the distance from the center to each focus.

Front

How do you determine the value of 'a' in a hyperbola?

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The value of 'a' is determined from the equation of the hyperbola, specifically from the denominators in the standard form.