Answer:
y²/19 -x²/36 = 1
Step-by-step 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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