Asked by Ally
Remove the xy-term by rotation of axes, reduce the resulting equation to standard form and trace the curve on the new axes: 13x^2-10xy+13y^2=72
Answers
Answered by
Steve
tan(2θ) = -10/0
2θ = -pi/2
θ = -pi/4
x' = (1/√2)x + (1/√2)y
y' = (-1/√2)x + (1/√2)y
13((1/√2)x + (1/√2)y)^2 - 10((1/√2)x + (1/√2)y)((-1/√2)x + (1/√2)y) + 13((-1/√2)x + (1/√2)y)^2 = 72
8x^2 + 18y^2 = 72
x^2/9 + y^2/4 = 1
http://www.wolframalpha.com/input/?i=plot+13x%5E2-10xy%2B13y%5E2%3D72%2C+y%3Dx%2C+y%3D-x
2θ = -pi/2
θ = -pi/4
x' = (1/√2)x + (1/√2)y
y' = (-1/√2)x + (1/√2)y
13((1/√2)x + (1/√2)y)^2 - 10((1/√2)x + (1/√2)y)((-1/√2)x + (1/√2)y) + 13((-1/√2)x + (1/√2)y)^2 = 72
8x^2 + 18y^2 = 72
x^2/9 + y^2/4 = 1
http://www.wolframalpha.com/input/?i=plot+13x%5E2-10xy%2B13y%5E2%3D72%2C+y%3Dx%2C+y%3D-x
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