Asked by Lost One
Convert this equation so that it could be entered into a calculator in the standard y= format. x^2 - 4xy + 4y^2 - 8y + 2 = 0
Answers
Answered by
Steve
First off, you can see that it's 2nd-degree in both x and y, so there is no simple y=f(x) expression. It's the equation of a rotated parabola, so there will be a top branch and a bottom branch.
Anyway, express it as a quadratic in y:
x^2 - 4xy + 4y^2 - 8y + 2 = 0
4y^2 - (4x+8)y + (x^2+2) = 0
Using the quadratic formula,
y = [(4x+8)±√((4x+8)^2 - 4(4)(x^2+2))]/8
= [x+2±√(4x+2)]/2
so, you can see there are two branches to the function.
Anyway, express it as a quadratic in y:
x^2 - 4xy + 4y^2 - 8y + 2 = 0
4y^2 - (4x+8)y + (x^2+2) = 0
Using the quadratic formula,
y = [(4x+8)±√((4x+8)^2 - 4(4)(x^2+2))]/8
= [x+2±√(4x+2)]/2
so, you can see there are two branches to the function.
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