Extension 2 finding Asymptotes Algebraically
To find asymptotes on a hyperbola x^2 - 4y^2 = 4
Differentiate
2x - 8y.dy/dx = 0
x/4y = dy/dx
y = ±sqrt(x^2 - 4)/2
dy/dx = ±x/2sqrt(x^2 - 4)
lim x -> inf. dy/dx = ±x/2x
= ±1/2
Therefore the gradient of the asymptotes is ±1/2