The Hyperbola - Problem 5

If a hyperbola is centered at the origin, we can write the equation in standard form if we know a vertex and a focus. The distance from the center (origin, in this case) to the focus is "c," and the distance from the center to the vertex is "a." Using the relationship a^2 + b^2 = c^2, we can find "b" as well. If the focus and vertex are along a horizontal line, then the x^2 term will be first in the hyperbola, but if the focus and vertex are along a vertical line, then the y^2 term will be first (as in this example.) Make sure you have a subtraction sign and the equation is set equal to one to keep the hyperbola in standard form.