## anonymous one year ago Find the vertices and foci of the hyperbola with equation quantity x minus five squared divided by eighty one minus the quantity of y minus one squared divided by one hundred and forty four = 1

1. anonymous

@saseal

2. anonymous

3. anonymous

$\frac{(x-5)^2}{81}-\frac{(y-1)^2}{4}=1$?

4. anonymous

this is way easier than you think but you need to know two things first a) the center and b) which way it is oriented

5. anonymous

I know that the hyperbolas are oriented left/right

6. anonymous

i thought ya all that earlier

7. anonymous

taught*

8. anonymous

center?

9. anonymous

@satellite73 you mean what i taught him?

10. anonymous

(0,5) ?

11. anonymous

12. anonymous

yes

13. anonymous

Ok so now what can I do?

14. anonymous

find c

15. anonymous

$\frac{(x-5)^2}{81}-\frac{(y-1)^2}{4}=1$$\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1$ what is $$a$$?

16. anonymous

Ok. c = 15

17. anonymous

a = 81, b =144

18. anonymous

no

19. anonymous

no

20. anonymous

$a^2=81,b^2=144$

21. anonymous

$c^2=a^2+b^2$

22. anonymous

thats why i told ya to put em into ^2 form

23. anonymous

Oh sorry. a = 9, b = 12

24. anonymous

Ok, so c = 15 because c^2 = 225

25. anonymous

@saseal

26. anonymous

yea?

27. anonymous

you know the hyperbola is transverse in x-axis so ( center +/- c, center) is your foci

28. anonymous

and same for the vertices

29. anonymous

Wait. These are my choices: A. Vertices: (17, 1), (-7, 1); Foci: (-7, 1), (17, 1) B. Vertices: (14, 1), (-4, 1); Foci: (-10, 1), (20, 1) C. Vertices: (1, 14), (1, -4); Foci: (1, -10), (1, 20) D. Vertices: (1, 17), (1, -7); Foci: (1, -7), (1, 17) So I know it has to be between A and B.

30. anonymous

Find an equation in standard form for the hyperbola with vertices at (0, ±3) and foci at (0, ±7). If my answer choices are: A. y squared over nine minus x squared over forty = 1 B. y squared over forty minus x squared over nine = 1 C. y squared over forty nine minus x squared over nine = 1 D. y squared over nine minus x squared over forty nine = 1 I was thinking it was between B and D.

31. anonymous

lemme check

32. anonymous

you see foci is c^2 = a^2+b^2 so we get 7^2 - 3^2 = 40

33. anonymous

Oh ok. So that would make it A.