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Find equations for the asymptotes of the hyperbola x2/9 - y2/81 = 1

Rewrite the equation as

(x/3)^2 - (y/9)^2 = 1

When both x and y are very large in absolute value, the "1" on the right is negligible in comparison, so y/9 approaches +/- x/3

The asymptotes are therefore
y = 3x and y = -3x.

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