Hyperbola Quiz 1

Using differential methods, find the formula with slope $\frac{dy}{dx} = 2x$.

$y = \frac{x}{2} + C$
$y = 2 + C$
$y = x^2 +C$
$y = x + C$

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

$\frac{b^2x}{a^2y}$
$\frac{(2x-a^2)b^2}{a^2y}$
$\frac{4xy}{a^2b^2}$
$\frac{a^2y}{b^2x}$

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

What is the equation of the graph $\frac{dy}{dx} = y^2x^2$?

$y = 2e{\frac{x^3}{3} + C}$
$y = – \frac{3}{x^3}$
$y = 2e{\frac{x^3}{3}}$
$y = – \frac{3}{x^3} + C$

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 hyperbola and your value for $\frac{dx}{dy} = \frac{b^2x}{a^2y}$ from quiz question 1 to find $\lim_{t \to \frac{\pi}{2}} \frac{dy}{dx}$.

$\frac{b}{a}$
$\frac{a}{b}$
$\frac{a^2}{b^2}$
$\frac{b^2}{a^2}$

Hyperbola

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