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A hyperbola centered at (5, 0) has a focus at (5, 10) and vertex at (5, 6). Which is the equation of the hyperbola in standard form?

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Final answer:

A hyperbola centered at (5, 0) with a focus at (5, 10) and a vertex at (5, 6) has the equation in standard form as (x-5)^2/a^2 - (y-0)^2/b^2 = 1, where a is the distance from the center to the vertex and b is the distance from the center to the foci.

Step-by-step explanation:

A hyperbola centered at (5, 0) with a focus at (5, 10) and a vertex at (5, 6) has the equation in standard form as

(x-5)2/a2 - (y-0)2/b2 = 1

where a is the distance from the center to the vertex and b is the distance from the center to the foci. In this case, a = 6-0 = 6 and b = 10-0 = 10, so the equation can be written as

(x-5)2/36 - (y-0)2/100 = 1

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