A hyperbola centered at the origin has vertices at (± √33,0) and foci at (± √59,0).

Write the equation of this hyperbola.

x^2/33 + y^2/26 = 1

Step-by-step explanation:

The formula for a hyperbola centered at the origin is:

x^2/a^2 - y^2/b^2 = 1

The vertices are located at (±a, 0), so we have that the value of a is √33

The foci are located at (±c, 0), where c^2 = a^2 + b^2

So if we have that c = √59, we can find the value of b:

59 = 33 + b^2

b^2 = 26

b = √26

So the formula for this hyperbole is:

x^2/33 + y^2/26 = 1