## cutiecomittee123 one year ago how do find the vertex and foci of this hyperbola (x-2)^2/36 - (y+1)^2/64 =1

1. misty1212

HI!!!

2. misty1212

standard form is $\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1$ you get the center with your eyeballs right?

3. misty1212

this is where you say "yes i see it" or "no i have no clue"

4. cutiecomittee123

yes:)

5. misty1212

ok what is the center?

6. cutiecomittee123

(2,-1)

7. misty1212

ok good now we need to know one other thing what does it look like left or right?|dw:1433186027332:dw|

8. cutiecomittee123

second, its horizontal

9. misty1212

hmmm no

10. misty1212

the $$x$$ term comes first, vertical

11. misty1212

now that we (presumably) have these two facts, the orientation and the center, the rest is easy

12. cutiecomittee123

oh gotcha

13. misty1212

the center is $$(2,-1)$$ and it is vertical that means the vertices are to the LEFT and RIGHT of the center (that is why we need the orientation first)

14. misty1212

if it was horizontal they would be up and down

15. cutiecomittee123

okay makes sense.

16. misty1212

you have $\frac{(x-2)^2}{36}-\frac{(y+1)^2}{64}=1$ which looks like $\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1$ what is $$a$$?

17. cutiecomittee123

a=6

18. misty1212

right so how easy is this? the vertices are 6 units to the right and left of $$(2,-1)$$

19. misty1212

got that ?

20. cutiecomittee123

okay so (-8, -1) and (5, -1)

21. misty1212

hmm no to the second one

22. misty1212

oh no no to both of them

23. misty1212

what is 6 units to the left of $$(2,-1)$$?

24. misty1212

or is simple english , what is $$2-6$$ and $$2+6$$?

25. cutiecomittee123

oh lol. (-4,-1) and (8,-1)

26. misty1212

whew!

27. cutiecomittee123

better?

28. misty1212

ok that takes care of the vertices now for the foci

29. misty1212

much yes

30. cutiecomittee123

alright so how do we find the foci?

31. misty1212

we need one number number , namely $$c$$ and we find it like pythagoras $a^2+b^2=c^2$

32. misty1212

you got $$a^2=36,b^2=64$$ what is $$c$$?

33. cutiecomittee123

so 36+64=100

34. misty1212

right and so $$c^2=100$$ making $$c=?$$

35. cutiecomittee123

c=10

36. cutiecomittee123

well + or - 10

37. misty1212

just plus

38. misty1212

so now (don't mess this up!) what is ten units to the right and left of $$(2,-1)$$?

39. cutiecomittee123

(12,-1) and (8,-1)

40. misty1212

lol

41. misty1212

i know what you meant (i hope)

42. misty1212

$(12,-1)$ is ten units the the right, $(\color{red}-8,1)$ is ten units to the left

43. cutiecomittee123

yeah :)

44. misty1212

ok that is it

45. cutiecomittee123

thank you :)

46. misty1212

it is really not that hard people here don't like it and math teachers make it seem way harder than it is you see we really only needed two things the center and the orientation

47. cutiecomittee123

yeah it seems simple

48. misty1212

$\color\magenta\heartsuit$