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**

- anonymous

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- 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

- Directrix

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

- 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

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## More answers

- anonymous

Eccentricity shall be given

- 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

- 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

- anonymous

Easy

- anonymous

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

- anonymous

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

- anonymous

Yep it changes orientation n xy plane

- anonymous

and how do i find that angle

- anonymous

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

- anonymous

how did you determine that?

- anonymous

how did i determine what?

- anonymous

that the angle is 45 degrees

- anonymous

slope of x-y=0

- 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

- 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

- Directrix

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

- anonymous

great answer

- anonymous

Thanx

- anonymous

what about this problem:

- anonymous

|dw:1328702038043:dw|

- anonymous

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

- anonymous

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

- anonymous

what angle do you get?

- anonymous

after doing :|dw:1328702371977:dw|

- anonymous

?

- anonymous

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

- anonymous

More complicated than appears origin is also shifted

- anonymous

No more ideas

- anonymous

i get -pi/12, but i am unsure

- anonymous

If it eliminates xy then it has to be the answer

- anonymous

but what is cos(-pi/12)

- anonymous

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

- anonymous

alright man thanks

- anonymous

cos(45-30)

- anonymous

but its -pi/12

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