The book’s notation is probably more standard that the notation I used, though both are acceptable. My reason for using a with x and b with y is that then my instruction to draw the box that defines the hyperbola is the same either way, the equations of the asymptotes are always y = +-b/a, and to sketch the hyperbola you need only determine which intersection points of the basic box with the coordinate axes actually occurs on the hyperbola (that will be the point for which the left-hand side is positive). The distance c of the focus from the center is the same with either convention. Sullivan’s choice is likely dictated by the desire to have the directrix at distance a^2 / c from the center, whichever way the hyperbola opens, and to have certain other equations that don’t depend on the direction in which the figure opens. With either convention, certain equations are the same both ways and others differ. Your solution to the problem is fine, and you are welcome to use whichever notation you find friendlier. I originally designed the course before I started using Sulllivan; don’t have the text I was using at the time handy or I’d check to see whether my convention agrees with that one or whether I am indeed oriented at a right angle to just about everyone else. Dave Smith Sir, In review for my test on Friday I noticed on CD # 2 track 16 that you express the Hyperbola as x^2/a^2 -y^2/b^2=1 and y^2/b^2-x^2/a^2=1. The latter y^2/b^2-x^2/a^2=1 is opposite what is stressed in the book. The have y^2/a^2-x^2/b^2=1. I was working the problem (y-4)^2/9 -(x-8)^2/24=36 and came up with (a)=18 and (b)=29.39 with c=34.47. My center was at (8,4), vertex at ((8,22) (x-h,a+y-k)) and my foci was (8,+-34.47).This Hyperbola was opening up and down with the y axis being the transverse axis. Could you tell me why they choose to express the equations different from your-self.