## iheartfood 2 years ago Write the equation for an ellipse with co-vertices (0,-3) and (0,3), major axis of length 10.

1. iheartfood

@jim_thompson5910 :)

2. jim_thompson5910

where is the center?

3. iheartfood

idk.. it doesn't say... it just says what i typed in :/

4. jim_thompson5910

i know, you have to find it

5. jim_thompson5910

the co-vertices lie along the minor axis

6. iheartfood

ok, how do we do that?

7. jim_thompson5910

the midpoint of this minor axis is where the center is

8. iheartfood

minor is vertical or horizontal?

9. jim_thompson5910

(0,-3) and (0,3) lie on what line?

10. iheartfood

so would the center be (0,0) ??

11. jim_thompson5910

yep

12. iheartfood

the x-axis?

13. jim_thompson5910

no, you have it flipped

14. iheartfood

okay so how do i write this equation?? oh the y axis?

15. jim_thompson5910

so the minor axis is vertical

16. jim_thompson5910

the major must be horizontal

17. iheartfood

ohh okay :) so its on the major axis?

18. jim_thompson5910

what is

19. iheartfood

(0,-3) and (0,3) ?

20. jim_thompson5910

no they are on the minor axis because they are co-vertices

21. jim_thompson5910

not vertices

22. iheartfood

ohh okay i see... what do we do now??

23. jim_thompson5910

how long is the minor axis?

24. iheartfood

idk :/ how do i find that?? i just know the major axis is 10...

25. jim_thompson5910

what's the distance between the co-vertices?

26. iheartfood

6? so is 6 the length of the minor axis?

27. jim_thompson5910

yes good

28. jim_thompson5910

cut that in half to get 3 that's the length of the semi-minor axis

29. jim_thompson5910

since the minor axis is vertical, this value of 3 corresponds to the value of b (which is paired with the y term below) (x-h)^2/(a^2) + (y-k)^2/(b^2) = 1

30. jim_thompson5910

so b = 3

31. jim_thompson5910

you know the center is (0,0) because you just found this, so (h,k) = (0,0)

32. iheartfood

okay :) so far we have this? (x-0)^2/(a^2) + (y-0)^2/(3^2)=1 ??

33. jim_thompson5910

good, the only thing you need is 'a'

34. iheartfood

how do we find that? do we square root 10? if so, can i just write sq.rt.10?

35. jim_thompson5910

no, the length of the major axis is 10 the length of the semi-major axis is ____

36. iheartfood

5?

37. jim_thompson5910

so a = 5

38. iheartfood

okay so is this my final equation??|dw:1356131103670:dw| is that it?? or do i need to simplify it more?

39. jim_thompson5910

you can simplify it more if you want

40. jim_thompson5910

|dw:1356131176856:dw|

41. iheartfood

but when it says write the equation, what format do they want it in?

42. jim_thompson5910

there are many formats, but that's probably the best one

43. jim_thompson5910

because you can tell it's an ellipse and you can use it to read off the center, major axis, minor axis lengths, etc etc

44. iheartfood

the simplified version?

45. jim_thompson5910

yeah

46. iheartfood

kk so we are done now?? htats it?

47. jim_thompson5910

yes

48. iheartfood

kk thank youu :)