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

Answer 1

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

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