1. Hyperbolas or

2. Definition of a Hyperbola The hyperbola is a locus of points in a plane where the difference of the distances from 2 fixed points, called foci, is always a constant. The points at which the two branches of a hyperbola are closest to each other are called the vertices. The center of a hyperbola is the midpoint of the vertices. F1F1 F2F2 d2d2 d1d1 VERTEX CENTER

3. Hyperbolas The standard form of a horizontally-oriented hyperbola with center (h, k) is; The equation for a vertically-oriented hyperbola with center (h, k) is; ) (

4. Hyperbolas asymptotes To graph a hyperbola by hand, you need to graph the asymptotes (guide lines). –The asymptotes go thru the CENTER (h,k) and have slope ±b/a. –Graph this equation: center –The center is (0,0). –The horizontal stretch is 2. –The vertical stretch is 3. –Draw the asymptotes. The foci are c from the center where a 2 + b 2 = c 2. aa b b b b c cc c F1F1 F2F2

5. Hyperbolas A vertically-oriented hyperbola graphs the same way except the foci are above and below the center. The hyperbola opens up and down.