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Remember that when the hyperbola is centered at the origin, the focal points are located either at (0, c) and (0, -c) or at (c, 0) and (-c, 0).

Recall that on the previous page, in the General Derivation of the standard equation section, b satisfied b2 = c2 - a2.

Rearranging this equation we arrive at c2 = a2 + b2.

Solving this for c, we get c = (a2 + b2)½.

We can now use this formula to calulate the location of the focal points.

EXAMPLE 1:
Given the equation x2/60 - y2/40 = 1, what is the location of the focal points?
Since the x2 term is positive and the y2 term is negative, we know that the hyperbola opens to the left and right. This means that the focal points will lie on the x-axis (since it's also centered at the origin).
We see by inspection that a2 = 60 and b2 = 40. Using this information in the formula defined above, we have:
c = (a2 + b2)½ c = (60 + 40)½ c = 100½ c = 10
Thus, the focal points are located at (10, 0) and (-10, 0).