SOLUTION: Find a new representation of {{{11x^2-50sqrt(3)xy-39y^2+576=0}}} after being rotated through an angle of 60 degrees. The question asks for the coefficient of {{{x^2}}}. I get -64,

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Find a new representation of {{{11x^2-50sqrt(3)xy-39y^2+576=0}}} after being rotated through an angle of 60 degrees. The question asks for the coefficient of {{{x^2}}}. I get -64,       Log On


   



Question 1141738: Find a new representation of 11x%5E2-50sqrt%283%29xy-39y%5E2%2B576=0 after being rotated through an angle of 60 degrees. The question asks for the coefficient of x%5E2. I get -64, but not sure if that's right. Thank you! Your work is much appreciated!
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
-64 is correct.
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For +Ax%5E2+%2B+Bxy+%2B+Cy%5E2+%2B+Dx+%2B+Ey+=+0++
rotated counter-clockwise by theta:

The leading coefficient in the rotated coordinates is:
A' = +Acos%5E2%28theta%29+%2B+Bsin%28theta%29cos%28theta%29+%2B+Csin%5E2%28theta%29+
=

= +%2811+-+150+-+117%29+%2F+4+