## anonymous 4 years ago Find the equation for the ellipse with foci (1,1) and (-1,-1) and major axis of length 4 **seems to shifted an angle in the xy coordinates**

1. anonymous

The question say to identify the type of conic section whose equation is given and find the vertices and foci, i am unsure wheter i should mention that its seems to on an angle or do i just go ahead and write down the equation for this ellipse

2. Directrix

Write the problem here exactly as the instructions appear in your book.

3. anonymous

identify the type of conic section whose equation is given and find the vertices and foci: Find the equation for the ellipse with foci (1,1) and (-1,-1) and major axis of length 4

4. anonymous

Eccentricity shall be given

5. anonymous

the only thing given was:Find the equation for the ellipse with foci (1,1) and (-1,-1) and major axis of length 4

6. anonymous

i have no problem finiding the equation, but its just that it looks tilted on the xy coordinate system, and i am wondering if i should find the angle its tilted on and how would i do so

7. anonymous

Easy

8. anonymous

$\frac{(x-y)^2}{16}+\frac{(x+y)^2}{8}=1$

9. anonymous

okay, but the titlted part, does that have any impact

10. anonymous

Yep it changes orientation n xy plane

11. anonymous

and how do i find that angle

12. anonymous

Angle of major axis with with horizontal is 45deg same as angle between x-y and x axis

13. anonymous

how did you determine that?

14. anonymous

how did i determine what?

15. anonymous

that the angle is 45 degrees

16. anonymous

slope of x-y=0

17. Directrix

Click the link to see the ellipse with equation: (x-y)^2/(16) + (x+y)^2/(8) =1 http://www.wolframalpha.com/input/?i=%28x-y%29%5E2%2F%2816%29+%2B+%28x%2By%29%5E2%2F%288%29+%3D1

18. anonymous

i see its shifted at what looks like a 45 degree angle, but i am still unclear how to determine its a 45 degree angle

19. Directrix

I would not worry about the angle. The instructions did not ask for it.

20. anonymous

21. anonymous

Thanx

22. anonymous

23. anonymous

|dw:1328702038043:dw|

24. anonymous

it says to Transform the following equatioon by a rotaion of axes into an equation that has no cross product term

25. anonymous

Put x=Xsin(t)-Ycos(t) y=Xsin(t)+Ycos(t) and solve for t

26. anonymous

what angle do you get?

27. anonymous

after doing :|dw:1328702371977:dw|

28. anonymous

?

29. anonymous

what angle do you get, you know the angle to plug into sin(t) and cos(t)

30. anonymous

More complicated than appears origin is also shifted

31. anonymous

No more ideas

32. anonymous

i get -pi/12, but i am unsure

33. anonymous

If it eliminates xy then it has to be the answer

34. anonymous

but what is cos(-pi/12)

35. anonymous

never mind ans will be accepted by your instructor any way it is

36. anonymous

alright man thanks

37. anonymous

cos(45-30)

38. anonymous

but its -pi/12