This is the equation of a hyperbola centered at the point (3, 2). In this standard form, the first term represents the horizontal distance while the second term signifies the vertical distance from the center to the vertices of the hyperbola. With horizontal transverse axis, the vertices can be located at (3 ± 6, 2) or (9, 2) and (-3, 2), making the hyperbola open to the left and right.

When dealing with hyperbolas, it’s common to misinterpret the relationship between the vertices and the focal points. Remember, the distance to the foci is related to the equation , where is half the distance between the vertices and is half the distance between the co-vertices. Always double-check your calculations to avoid errors in identifying these crucial points.