Question 1120791: Rotate the axes to eliminate the xy-term in the equation.Then write the equation in standard form. Sketch the graph of the resulting equation, showing both sets of axes.
b. xy – 2y – 4x = 0
Answer by Alex.33(110)   (Show Source):
You can put this solution on YOUR website! To rotate axes by a radians (note that a is confined within (0, pi))(Personally I'd like to do it counterclockwise, but you're free to do otherwise), you'll need to convert the coordinates accordingly, which can be proved with a little simple geometry.
x=x'cosa-y'sina
y=x'sina+y'cosa
Put them into the equation you gave:
sina*cosa*(x'^2-y'^2)+((cosa)^2-(sina)^2)x'y'-2(x'sina+y'cosa)-4(x'cosa-y'sina)=0
Aha! To succeed, we just need to get the coefficient of the term x'y' equal to 0.
(cosa)^2-(sina)^2=cos(2a)=0.
a=pi/4 or 3pi/4.
And it's done.
//SORRY FOR THE ERROR WITH THE FOMULA GENERATOR.
Wanna know more? check this out http://www.sparknotes.com/math/precalc/conicsections/section5/#_motz_
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