randRange( 2, 9 ) randRange( 2, 9 ) randRange( -9, 9 ) randRange( -9, 9 ) rand(2) WHICH_NEG === 1 ? "+" : "+" WHICH_NEG === 1 ? "" : "-" 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 hyperbola H is WHICH_NEG == 1 ? expr(["-", Y2T, X2T]) : expr(["-", X2T, Y2T]) = 1.

What are the asymptotes?

y = \pm (B/A )(x + -H ) + K

enter integers, simplified fractions, or exact decimals for each term

pay attention to the sign of each number you enter to be sure the entire equation is correct

We want to rewrite the equation in terms of y, so start off by moving the y terms to one side:

 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 of both sides.

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

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

As x approaches positive or negative infinity, the constant term in the square root matters less and less, so we can just ignore it.

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

plus( "y", -K ) \approx \pm \left(\dfrac{B \cdot (plus( "x", -H ))}{ A }\right)

Add K to both sides and rewrite Subtract -K from both sides and rewrite Rewrite as an equality in terms of y to get the equation of the asymptotes:

y = \pm \dfrac{reduce( A, B )[1]}{reduce( A, B )[0]}(plus( "x", -H ))K >= 0 ? "+" : "" K