1. March 27 th copyright2009merrydavidson

2. HYPERBOLA’S A hyperbola looks sort of like two mirrored parabolas.parabolas The two "halves" being called "branches". A hyperbola has two foci and two vertices. Hyperbola’s also have asymptotes.

3. HYPERBOLA’S Definition: The set of all points for which the difference in the distance to two fixed points (called the foci) is constant.setpoints foci

4. Horizontal Hyperbola d2d2 d1d1 d 1 -d 2 = constant

5. Horizontal Hyperbola d2d2 d1d1 d 1 -d 2 = constant

6. Horizontal Hyperbola d2d2 d1d1 d 1 -d 2 = constant

7. Horizontal Hyperbola c = center to focus b = center to box a = center to vertex “x” term is positive

8. Major/Transverse axis goes through vertices. Minor/Conjugate axis a b c asymptote HORIZONTAL hyperbola

9. Vertical Hyperbola c = center to focus b = center to box a = center to vertex “y” term is positive

10. Major/Transverse axis goes through vertices. Minor/Conjugate axis b a c asymptote Vertical Hyperbola

11. Horizontal Hyperbola Vertical Hyperbola c 2 = a 2 + b 2 SUMMARY MAJOR axis does NOT mean longer.

12. Ex 1: Horizontal/Vertical?Center: a 2 =a= b 2 =b= c (-1,3) 25 5 93 c 2 = a 2 + b 2 Let’s draw what we know so far…

13. Draw in the box. Ex 1: Draw in the asymptotes. Draw in the branches. Place “c” on the graph. F1: F2:

14. Ex 2: Horizontal/Vertical?Center: a 2 =a= b 2 =b=c = (0,1) 25 5 42 c 2 = a 2 + b 2 Let’s draw what we know so far… Insert a “4” on your notes!

15. Draw in the box. Ex 2: Draw in the asymptotes. Draw in the branches. Place “c” on the graph. F1: F2:

16. Ex 3:Find the center, foci, and the equation of the asymptotes. Center: Major axis: horizontal or vertical a = Vertices b = c =Foci 4x 2 – y 2 - 16x - 4y -4 = 0 (2,-2) (4,-2),(0,-2)

17. Ex 4: Find the equation of the hyperbola if the vertices are at (5,0) and (-5,0) and b 2 = 49. Draw in what you know. Where is the vertex? (0,0) Major axis: H or V? Fill in the equation.

18. Ex 5. Write the equation for the hyperbola graphed on your notes.

19. HW: WS 10-5