SOLUTION: identity the conic whose equation is 9x²-10xy-4y²-36=0 by rotating the xy-axes to put the conic in standard position.

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Question 1150091: identity the conic whose equation is 9x²-10xy-4y²-36=0 by rotating the xy-axes to put the conic in standard position.

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
9x²-10xy-4y²-36=0

Ax²+Bxy+Cy²+Dx+Ey+F=0

The discriminant B²-4AC = (-10)²-4(9)(-4) = 100+144 = 244 > 0 so it is
the equation of a hyperbola.



We calculate the angle through which to rotate the xy-axes.

The y-axis must be rotated through an angle of θ where

cot%282theta%29=%28A-C%29%2FB=%289-%28-4%29%29%2F%28-10%29=-1.3
2theta=127.568592
theta=63.78429601

The x-axis must be rotated through an angle of 90°-θ = 26.21570399.

Edwin