## anonymous one year ago What are the foci of the following graph?

1. anonymous

the asymptotes is 0/-20

2. anonymous

im lost

3. anonymous

well wait

4. anonymous

c2=0+20^2 c2=0+400 c=20

5. Michele_Laino

the general formula, is: $\Large {c^2} = {a^2} + {b^2}$ if, the hyperbola is represented as by the subsequent equation: $\Large \frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1$

6. anonymous

x2+y2/20=1

7. Michele_Laino

from your graph, I see that: $\Large 2a = 10$

8. anonymous

x2/25+y2/20=1

9. Michele_Laino

and: $\Large 2b = 4$

10. Michele_Laino

2b is the height of the dashed rectangle

11. Michele_Laino

so: $\Large a = 5,\quad b = 2$

12. anonymous

x2/25+y2/4=1

13. Michele_Laino

I think it is: $\Large \frac{{{x^2}}}{{25}} - \frac{{{y^2}}}{4} = 1$

14. anonymous

if it was an ellipses it be +

15. Michele_Laino

your graph is a hyperbola, not an ellipse

16. anonymous

ik, i was jsut saying to make sure i know the difference ellipse is + hyperbola is -

17. anonymous

right?

18. Michele_Laino

ok! right!

19. anonymous

okay. now i have another question that uses the same graph, can we just solve it here if thats okay?

20. Michele_Laino

ok!

21. anonymous

what is the equation of the graph?

22. Michele_Laino

I wrote that equation before: $\Large \frac{{{x^2}}}{{25}} - \frac{{{y^2}}}{4} = 1$

23. anonymous

its the saem for the foci and equation?

24. anonymous

same*

25. Michele_Laino

the equation for the foci is: $\Large {c^2} = {a^2} + {b^2} = 25 + 4 = ...$

26. Michele_Laino

what is c?

27. anonymous

29

28. Michele_Laino

more precisely we have: $\Large c = \pm \sqrt {29}$

29. anonymous

okay i see i see

30. Michele_Laino

so the requested foci are the subsequent points: $\Large \begin{gathered} {F_1} = \left( { - \sqrt {29} ,0} \right) \hfill \\ {F_2} = \left( {\sqrt {29} ,0} \right) \hfill \\ \end{gathered}$

31. anonymous

okay. thank you. now ill start a new post bc i hav another question, or can we keep going here? its all up to u if u want more medals

32. Michele_Laino

please we have to make a traslation, since that equation above is referring to a hyperbola centrered at the origin of our system of coordinates

33. anonymous

okay. how do we do that?

34. Michele_Laino

from you graph, we can note that the center of our hyperbola is located at the center of the dashed rectangle, which is the point (2,1)

35. anonymous

okay.

36. Michele_Laino

oopss... (1,2) not (2,1)

37. anonymous

lol okay, what next?

38. Michele_Laino

in other words, the equation of our traslation, is: $\Large \left\{ \begin{gathered} x = X + 1 \hfill \\ y = Y + 2 \hfill \\ \end{gathered} \right.$ where X,Y is the new coordinates system located at (1,2)

39. anonymous

x=2? y=4?

40. Michele_Laino

|dw:1439649900978:dw|

41. anonymous

okay

42. Michele_Laino

so the coordinates of the foci referred to the X,Y system are: $\Large \begin{gathered} {F_1} = \left( { - \sqrt {29} ,0} \right) \hfill \\ {F_2} = \left( {\sqrt {29} ,0} \right) \hfill \\ \end{gathered}$ whereas the coordinates of the foci referred to the x,y system are: $\Large \begin{gathered} {F_1} = \left( { - \sqrt {29} + 1,2} \right) \hfill \\ {F_2} = \left( {\sqrt {29} + 1,2} \right) \hfill \\ \end{gathered}$

43. Michele_Laino

namely I have applied the traslation: $\Large \left\{ \begin{gathered} x = X + 1 \hfill \\ y = Y + 2 \hfill \\ \end{gathered} \right.$

44. Michele_Laino

for example, let's consider F1

45. Michele_Laino

we have: $\Large X = - \sqrt {29} ,\quad Y = 0$ am I right?

46. anonymous

yes

47. Michele_Laino

ok! now I apply my traslation, so I get: $\Large \left\{ \begin{gathered} x = X + 1 = - \sqrt {29} + 1 \hfill \\ y = Y + 2 = 0 + 2 = 2 \hfill \\ \end{gathered} \right.$

48. Michele_Laino

similarly for F2

49. anonymous

okay so which will the anwser be? or are we not there yet.

50. Michele_Laino

your answer is: "The coordinates of the foci, of our hyperbola, are: $\Large \begin{gathered} {F_1} = \left( { - \sqrt {29} + 1,2} \right) \hfill \\ {F_2} = \left( {\sqrt {29} + 1,2} \right) \hfill \\ \end{gathered}$" that's all!

51. anonymous

so -squ29 +1,2 and squ29 +1,2

52. Michele_Laino

yes!

53. anonymous

thank you! now cn we move on or do u want me to start a new post?

54. Michele_Laino

55. anonymous

i have like 3 more about hyperbola and then im done

56. Michele_Laino

if the hyperbola is different I think it is better if you open a new question

57. anonymous

okay.