Determine the appropriate rotation formulas to use so that the new equation contains no xy-term.
(1) x^2 - 4xy + y^2 - 3 = 0
(2) 3x^2 - 10xy + 3y^2 - 32 = 0
Hello, magentarita!
I'll walk through the first one . . .
Given the general quadratic: .Determine the appropriate rotation formulas to use
so that the new equation contains no -term.
. . the angle of rotation is given by: .
. . and the new coordinates are: .
We have: .
. . Then: .
. . Hence: .
And we have: .
Substitute into: .
. .
. .
. .
. .
. .