## cutiecomittee123 one year ago how do i find the foci of an elipse?

1. amistre64

do you know where the center and vertexes are?

2. amistre64

if so, then the foci are an odd construction of the usual pythag thrm ... in this case, b and c are legs, and a is a hypotenus giving us a rather strange look of c^2 + b^2 = a^2, such that x is the distance from center to focus

3. cutiecomittee123

well the equation i have is (x+2)^2/9+(y-4)^2/36=1

4. amistre64

then we know a^2 and b^2, right?

5. cutiecomittee123

yes

6. amistre64

so show me c^2 :)

7. cutiecomittee123

36+ =9 c^2=25

8. cutiecomittee123

-25

9. amistre64

36 - 9 = 27

10. cutiecomittee123

oh yeah lol

11. amistre64

so 3cbrt3 = c, or this distance from center.

12. amistre64

3 sqrt3 lol

13. amistre64

so, tell me our center, and in what direction we need to move

14. cutiecomittee123

center (-2,4) we move left and right

15. amistre64

not left and right notice that under y is bigger than under x y is bigger than x, so our focuses are going to be in relation to y |dw:1433524715502:dw|

16. cutiecomittee123

so (-2, 4+ or - 3sqrt3)

17. amistre64

yes

18. cutiecomittee123

alright

19. cutiecomittee123

thanks:)

20. amistre64

youre welcome

21. cutiecomittee123

can you help me with one other thing

22. amistre64

depends on what it is and how good my memory is :)

23. cutiecomittee123

finding the eccentricity of (x+7)^/16+(y-3)^2/4=1

24. amistre64

define the formula for eccentricity

25. cutiecomittee123

eccentricity = c/a

26. amistre64

thats what i thought so sqrt(c^2/a^2) should work .. c^2 is the difference of the bottoms, and a^2 is the larger of them

27. cutiecomittee123

So sqrt 12/4

28. amistre64

um, 16 is bigger than 4

29. cutiecomittee123

because sqrt 16 is 4

30. amistre64

oh, youve got some notation off then sqrt(12/16) sqrt(3/4) sqrt(3)/2

31. cutiecomittee123

Wait I dont get how you reduced those? wouldnt it just be sqrt(3/4)

32. cutiecomittee123

Like why did you reduce so far?

33. amistre64

thats what you do with fractions, you reduce them till they have no common factors

34. cutiecomittee123

makes sense.

35. cutiecomittee123

So final answer is sqrt (3/2)

36. amistre64

$\sqrt{\frac{16-4}{16}}$ $\sqrt{\frac{12}{16}}$ $\sqrt{\frac{4*3}{4*4}}$ $\sqrt{\frac{3}{4}}$ $\frac{\sqrt3}{\sqrt4}$

37. cutiecomittee123

then reduce? or

38. amistre64

can it be simplified more?

39. amistre64

i just showed you some of the process, i didnt finish it ... i figured youd be cognizant enough to see where its going.

40. cutiecomittee123

yea sqr t4 is equal to 2

41. amistre64

then lets go with sqrt(3) /2

42. cutiecomittee123

Then you have sqrt(3/2) :) thanks

43. amistre64

no, not sqrt (3/2) im not sure if its a typing error of yours, or if you are making a mistake. it is: sqrt(3) ------ 2

44. amistre64

sqrt(3) sqrt(3) ----- = ----- sqrt(4) 2

45. cutiecomittee123

yeah thats how I percieved it and meant it

46. amistre64

good luck :)