Babynini one year ago Ellipses

1. Babynini

2. Babynini

@freckles

3. Babynini

@rational

4. Babynini

oh I know where I calculated wrong. in that c/a and forgot that a was =4 and not 2

5. Babynini

would it be b^2 = 2?

6. Babynini

nope that's not right either.

7. Babynini

@rvc do you know how to do these?

8. Babynini

@jim_thompson5910

9. rvc

bad at circle and conics sorry :(

10. Babynini

Thanks for looking at it though. Ah well.

11. rvc

12. Babynini

first off we find a from the major axis a= 4 then we find c by looking at the eccentricity c/a = sq7/2

13. anonymous

focii on y axis means that the major axis is on Y aix and you are given with the length of major axis and ecc.. you can find minor axis from that data

14. anonymous

axis**

15. alekos

It would have a vertical major axis so (x-h)^2/b^2 + (y-k)^2/a^2 =1 where 2b=8

16. Babynini

how do I find the minor axis in there?

17. alekos

eccentricity = sqrt(a^2-b^2)/a

18. anonymous

b^2 = a^2(1-e^2)

19. alekos

so from this you can find the minor axis

20. Babynini

hmm

21. alekos

focii are on the y-axis so h=0

22. Babynini

so x^2/8 + y^2/16 = 1

23. Babynini

24. Babynini

@iambatman save me. lol

25. anonymous

Hollllllaaaa

26. Babynini

aloo

27. anonymous

major axis = 8 ye?

28. Babynini

I just need to find an equation :P

29. Babynini

yeah

30. Babynini

major axis = 2a so a = 4

31. anonymous

Yes good :P $e = \frac{ c }{ a } ~~~\text{and}~~~ c^2 = a^2-b^2$ yes yes this looks good, it will work out nicely

32. anonymous

Ok so notice we're given the eccentricity (e) and it tells us the Foci is on the y - axis, this is important because the foci are ALWAYS on the major axis. So will the major axis run vertically or horizontally?

33. Babynini

vertically?

34. anonymous

That sounds good, so what should we do next

35. anonymous

You should already realize an error in your work with that information

36. Babynini

a should be the bigger one?

37. anonymous

You're too good :)

38. Babynini

Aw, shucks.

39. Babynini

so what numbers do i flip around?

40. anonymous

Well lets find b first

41. anonymous

To do that we have $e = \frac{ c }{ a }$ and $c^2 = a^2 - b^2$

42. Babynini

e = sq7/2 but we're given that a = 4 so do we double that whole thing?

43. anonymous

What was that cute game we were playing earlier? I had a name for it

44. Babynini

lol substitution?

45. anonymous

Yeah that's it ;)

46. Babynini

but we're given the e!

47. anonymous

So what's stopping you from solving for c :)

48. Babynini

no b?

49. anonymous

We have a and e!

50. Babynini

ooh oh

51. Babynini

sq7/2=c/4

52. anonymous

:))))

53. anonymous

So what will be our c value?

54. Babynini

sq14?

55. Babynini

$2\sqrt{7}$

56. anonymous

Looks good, now what's our next step :)

57. Babynini

find b!

58. anonymous

Right, and how will we do that

59. Babynini

so that's just c, not c^2

60. anonymous

Yes good observation!

61. Babynini

so now c^2=a^2+b^2

62. anonymous

Stop right there for a second!

63. Babynini

o.o yes sir.

64. anonymous

Lets look at the equation you said, what is that for :)

65. Babynini

c

66. anonymous

ircle

67. Babynini

lol

68. anonymous

That's where a lot of people make mistakes, for an ellipse it's $c^2 = a^2 - b^2$

69. anonymous

Note the negative sign

70. Babynini

o.o gasp. that is no bueno.

71. Babynini

b^2=a^2-c^2 then

72. anonymous

:), now remember as I always say it's a game of substitution

73. Babynini

$b^2 = 16 - (2\sqrt{7})^2$

74. Babynini

$b^2 = 16-28$ $b^2=-12$

75. Babynini

$b=\sqrt{12}$

76. anonymous

No, the negative is there, something is wrong

77. anonymous

Err, $e = \frac{ c }{ a } \implies c = e \times a \implies c = \frac{ \sqrt{7} }{ 4 } \times 4 \implies \sqrt{7}$ bleh :)

78. Babynini

..oh hehe

79. anonymous

I guess I should be doing the math as well haha

80. Babynini

sorry!

81. Babynini

ai ai ai I need to go to bed soon. waay to early on a school night =.= and you do too.

82. anonymous

No it's alright we just had mistaken the eccentricity we had sqrt(7)/2 when it's 4 :P

83. Babynini

oh xD

84. anonymous

Don't worry about me :), I'm the dark knight, night is where I work muahah!

85. Babynini

right, right, how could I forget!

86. anonymous

Alright so lets find b again bleh :)

87. anonymous

$b^2 = a^2-c^2$

88. anonymous

$a = 4~~~c = \sqrt{7}$

89. Babynini

b = 3

90. Babynini

b^2 = 9

91. anonymous

Now that looks good

92. Babynini

so..the answer I had at the very beginning. Look at the screenshot thing =.=

93. anonymous

major axis runs vertically :P

94. Babynini

ooh myy goooshh aspidghpaihgpi

95. Babynini

fricken hour later hahahah

96. anonymous

It's ok, the struggle is more important than the final answer, you will remember how to do it now :)

97. Babynini

we're geniuses! :)

98. Babynini

for sure though!

99. anonymous

Not me, you are a genius! You deserve a fields medal hehe!

100. Babynini

noo no bro the answers wrong still D:

101. anonymous

What did you put

102. Babynini

103. anonymous

Nope.

104. anonymous

a = 4, a^2 = 16

105. Babynini

...can you write out the whole answer just so i make sure to put it right?

106. anonymous

and y runs vertically hence $\frac{ x^2 }{ 9 }+ \frac{ y^2 }{ 16 } = 1$

107. Babynini

That little green mark though :')

108. anonymous

Yes, sorry about that I did not check if you put a^2

109. Babynini

it's all good :) so it was indeed my first answer just forgot to ^2 the a

110. anonymous

Yes, we just had to switch it around, but in a test you would have to show your work, and you now know how to do that! :) It's a game of substitution as always!

111. Babynini

haha cuz we hate the players (not really) but love the game ;)

112. Babynini

yes indeed!

113. Babynini

*hug hug hug. you are a trooper. haha and with that. I am off to bed.

114. anonymous

Take care :)

115. Babynini

Night, Batman.