CK-12-Pre-Calculus Concepts

http://www.ck12.org Chapter 9. Conics

Since 3, 4, 5 is a well known Pythagorean number triple it should be clear to you thata= 12 ,b= 9.
(x 12 + 22 )^2 −(y− 925 )^2 = 1

Practice

Use the following equation for #1 - #5: x^2 + 2 x− 4 y^2 − 24 y− 51 = 0

1. Put the hyperbola into graphing form. Explain how you know it is a hyperbola.


2. Identify whether the hyperbola opens side to side or up and down.


3. Find the location of the vertices.


4. Find the equations of the asymptotes.


5. Sketch the hyperbola.
   Use the following equation for #6 - #10:− 9 x^2 − 36 x+ 16 y^2 − 32 y− 164 = 0


6. Put the hyperbola into graphing form. Explain how you know it is a hyperbola.


7. Identify whether the hyperbola opens side to side or up and down.


8. Find the location of the vertices.


9. Find the equations of the asymptotes.


10. Sketch the hyperbola.
    Use the following equation for #11 - #15:x^2 − 6 x− 9 y^2 − 54 y− 81 = 0


11. Put the hyperbola into graphing form. Explain how you know it is a hyperbola.


12. Identify whether the hyperbola opens side to side or up and down.


13. Find the location of the vertices.


14. Find the equations of the asymptotes.


15. Sketch the hyperbola.