Question: what is the standard form of hyperbola?
Answer: The standard form of a hyperbola that opens sideways is (x - h)^2 / a^2 - (y - k)^2 / b^2 = 1. For the hyperbola that opens up and down, it is (y - k)^2 / a^2 - (x - h)^2 / b^2 = 1. In both cases, the center of the hyperbola is given by (h, k). The vertices are a spaces away from the center.