randRange( 2, 9 ) randRange( 2, 9 ) randRange( -9, 9 ) randRange( -9, 9 ) rand(2) WHICH_NEG === 1 ? "+" : "+" WHICH_NEG === 1 ? "" : "-" plus( "\\dfrac{" + expr( ["*", reduce( A, B )[1] , plus( "x", -H ) ] ) + "}{" + reduce( A, B )[0] + "}", K) B+"*(-" + H + "+x)/" + A + "+" + K H === 0 ? "x^2" : expr(["^", ["+", "x", -H], 2]) K === 0 ? "y^2" : expr(["^", ["+", "y", -K], 2]) H === 0 ? "\\dfrac{x^2}{" + A*A + "}" : "\\dfrac {" + expr(["^", ["+", "x", -H], 2]) + "}{" + A*A +"}" K === 0 ? "\\dfrac{y^2}{" + B*B + "}" : "\\dfrac {" + expr(["^", ["+", "y", -K], 2]) + "}{" + B*B +"}"

The equation of a hyperbola H is WHICH_NEG == 1 ? expr(["-", Y2T, X2T]) : expr(["-", X2T, Y2T]) = 1.

What are the asymptotes?

y = \pm ANSWER

We first rewrite the equation in terms of y.

Y2T = Y_MINUS 1 X_MINUS X2T

Multiply both sides of the equation by B * B.

Y = { Y_MINUS B*B X_MINUS \dfrac{ X \cdot B*B }{ A*A }}

Take the square root.

plus("y", -K) = \pm \sqrt { Y_MINUS B*B X_MINUS \dfrac{ X \cdot B*B }{ A*A }}

As x approaches infinity, the constant matters less and less.

plus("y", -K) \approx \sqrt { \dfrac{ X \cdot B*B }{ A*A }}

Therefore, the asymptotes are y \pm ASYMPT