the following equation is a hyperbola,
5x^2 + 38x - 8xy - 22y - y^2 + 47 = 0
and i need to know how to translate and rotate it so that it is in the standard form, AX^2 + BY^2 = 1
does anyone have any ideas??? any help would be great.
i don't think i need any trig equations, my lecturer said to use a diagonalise function, using eigenvales and vectors. but i dont know how to 'translate' the function so that it can be rotated using eigenvalues. etc. cheers anyway. could u possibly suggest anything else.
Let's see what you get.
sorry for not being more clearer, i hope my second post didn't sound nasty because that wasn't intended. anyway thanks for that link very useful however it doesn't consider the 38x and 22y term could you possibly help me there. i hope im being clear. lol
Then the conic can be expressed in matrix form as .
Let where is a column matrix to be determined. Then and so:
(since is real symmetric) where .
Since is invertible there exists a unique matrix such that . With this choice of you have:
The substitution corresponds to a translation of the origin to the point with coordinate matrix .
All the dirty calculational details are left to you ......
Otherwise, I get the gist and it looks good.
One thing ....
I'd write it as etc. where and are the rotated coordinates.
And you understand the relationship between the unrotated coordinates and the rotated ones ..... where P is as defined in the link I gave you and .
For practice, I'd advise checking using the technique TKHunny initially suggested .....
(Caveat emptor: My arithmetic is as bad as anyone's ..... but I'm pretty sure everything (that is, C, etc.) is OK. And, since I'm lazy, I checked the eigenvalues using my TI-89 so I'm certain they're OK!)