Math 1715, L. Brown Section 12.3: Hyperbolas A hyperbolais the set of all points in the plane the differenceof whose distances from two fixed points (foci) is constant. Standard Equations of Hyperbolas Centered at (0, 0) 12222byax12222bxayTransverse axis: x-axis Transverse axis:y-axis Asymptotes: xabyAsymptotes:xbayFoci:(c, 0) and (–c, 0) Foci:(0, c) and (0, –c) a= distance between center and a vertex c= distance between center and a focus Relationship: 222acb(or 222bac) The asymptotes can be drawn by using the diagonals of a rectangle with corners found using aand b. The centeris the midpoint between the two foci. The line containing the foci is called the transverse axis. The line through the center and perpendicular to the transverse axis is the conjugate axis. The verticesare the two points where the curve intersects the transverse axis.