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