Question

A hyperbola centered at the origin has vertices at (0,±sqrt(19)) and foci at (0,±sqrt(55)).

Write the equation of this hyperbola.

Answer 1

y²/19 -x²/36 = 1

Explanation:

You want the equation of a hyperbola centered at the origin with vertices at (0,±sqrt(19)) and foci at (0,±sqrt(55)).

Equation of a hyperbola

If a, f are the distances from center (the origin) of the vertices and foci, the equation of the hyperbola with vertices on the y-axis can be written as ...

y²/a² -x²/(f²-a²) = 1

For a=√19 and f=√55, the equation is ...

y²/19 -x²/36 = 1

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