Problem: Find the asymptotes of the hyperbola 4x^2 + 5xy + y^2 = 10.

The book says to rearrange this

equation to y^2 + (5x)y + (4x^2 - 10) = 0, then use the

quadratic formula, (-5x +/- sqrt(25x^2 - 4 (4x^2 - 10)))/2. Simplifying a bit to get

(-5x +/- sqrt (9x^2 - 40))/2. Then the book factors out 3x from the sqrt to get (-5x +/- 3x sqrt(1 - 40/9x^2))/2. I got it up to this point.

Then the book says the 40/9x^2 term approaches zero as x -> inf, which I agree with, to get y = (-5x +/- 3x)/2. Why are the -5x and 3x terms ignored when applying the x -> inf?

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