Hyperbola Quiz 1

What is $\frac{dx}{dy}$ given $\frac{x^2}{a^2} – \frac{y^2}{b^2} = 1$?

Sketch the slope field associated with your answer from the previous question ($\frac{dy}{dx} = \frac{b^2x}{a^2y}$) when $ a = b = 1$.

Given the parametric definition of a hyperbola $x = a*\sec(t), y = b*\tan(t)$, graph this for when $ a = b = 1$ over $0 \leq t \leq 2\pi$.

Use the parametric definition of the parabola and your value for $\frac{dx}{dy}$ from quiz question 1 ($\frac{b^2x}{a^2y}$) to find $\lim_{t \to \frac{\pi}{2}} \frac{dy}{dx}$.