Subject: Math problem!

I'm not a geometry specialist, but I'm doing my Math PhD, so maybe I can help ;-)

ok, I solved my first problem, but I have a bunch of those coming soon. but its kinda difficult to translate em to english:S


u r 1st, 2nd 3rd year math guy?

It's the first year of my PhD ;-)

i can count to potato.

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Only english please guys

find the canonical equatation of Γ={(x,y):2x**2 - 12xy - 7y**2 + 8x +6y = 0}

any idea?:l

i know im really helping.

I don't know what the canonical equation is exactly (in general). I'm guessing it's the equation of an ellipse or something like that (because it's the equation of a circle with an x-y-interference.

yea, it is ellips/circle/parabola/hyperbola stuff

Did you have similar exercises like this one? Usually when dealing with quadratic forms you look at the eigenvalues of the related matrices to see which geometrical object you have. In this case you would probably do a couple of transformations of the coordinates, depending on the eigenvalues and -vectors, but I'm not an expert on this subject ;)

the coefficients look nasty, but you can try:P
canonical form is: X**2/A + Y**2/B + C = 0
First, let's write it in this way:
a11*x**2 + 2*a12*x*y + a22*y**2 + 2*a13*x + 2*a23*y + a33 = 0
Identifying the terms, we'll have:
a11=2, a12=a21=-6, a22=-7, a23=a32=3, a13=a31=4.
second step is to calculate the discriminants:
D(aij) i,j=1,2,3 and d(aij) i,j = 1,2
and the invariant: I = a11+a12 = -4
Third step is to calculate the solutions of the characteristic equation:
n**2 - I*n + d = 0, with solutions n1 and n2
finally, you can write the canonical form so:
n1*X**2 + n2*Y**2 + D/d = 0


(edited)

oh, i forgot - after you calculate the discriminants, check d ≠ and D≠ 0

can anyone help me with descrete elements of math?

I mean elements of discrete math