Expert: Sherry Wallin - 4/15/2009

Question
Hello homeschool parent again I need ur help u guys have been great and patient with me thanx so can u plaease answer these for me


For the hyperbola  4y^2 - 9x^2 = 36

1. Which way does it open?
2. What are the coordinates of the foci?
3. What are the coordinates of the vertices?
 
                                   y^2
For the hyperbola  x^2 - -------- = 1
                                       2
4. Which way does it open
5. What are the coordinates of the foci?
6. What are the coordinates of the vertices?


For the hyperbola  (x - 2)^2    (y - 1)^2
                          --------------- - -------------- = 1
                                 4               9
7. Which way does it open?
8. What are the coordinates of the vertices?

What are the equations of the following hyperbolas?
9. Center at (0,0); opens vertically; a=3, b=4

10. Center at (0,0); opens horizontally; a = sqr root of 5, b = 2

11. Center at (0,0) opens horizontally; a=1, b=3

12. Foci (0,13), (0,-13); vertices (0,5),(0,-5)

13. Foci (10,0),(-10,0); vertices (8,0),(-8,0)

14. Foci (5,0), (-5,0); vertices (3,0),(-3,0)

15. Center at (3,2); vertices (0,2), (6,2); b=4

16. Center at (-1,1); vertices (-1,5), (-1,-3); foci
(-1,6), (-1,-4)


Yes/No questions

17. Is (4 sqr root 2, 3) a point on a hyperbola
      x^2/16 - y^2/9 = 1

18. Is (10,14) a point on the hyperbola
       y^2/ 64 - x^2/100 = 1

19. Is (-8 sqr root 2, -6) a point on the hyperbola
       x^2/64 - y^2/36 = 1

Answer
Hi as usual I will answer a few of these questions:

17 - [(4*sqrt2)^2]/16- (3^2)/9 = [16*2]/16 -9/9 = 32/16 - 1 = 2-1 =  1
thus 4 sqr root( 2, 3) is a point on the hyperbola x^2/16 - y^2/9 = 1

18 - (14^2)/64 -10^2/100 = 289/64- 1 = 225/64 != 1 so (10,14) is NOT a point on the hyperbola  y^2/ 64 - x^2/100 = 1

19 - [(-8*sqrt 2)^2]/64 -[(-6)^2]/36 = 64*2/64 -36/36 = 2-1 = 1 so
(-8 sqr root 2, -6) is a point on the hyperbola x^2/64 - y^2/36 = 1.

Math Prof