Question

Find the slope of the graph of the equation at the given point. (If an answer is undefined, enter UNDEFINED.)

Answer 1

Answer:

Undefined.

Step-by-step explanation:

We want to find the slope of the graph of the equation:

$\displaystyle x^2 - y^2 = 81$

At the point (9, 0).

In other words, we want to evaluate dy/dx when x = 9 and y = 0.

Find dy/dx. We can take the derivative of both sides with respect to x:

$\displaystyle \begin{aligned} \frac{d}{dx}\left[ x^2 - y^2\right] = \frac{d}{dx}\left [ 81\right] \\ \\ 2x - 2y \frac{dy}{dx} &= 0 \\ \\ \frac{dy}{dx} = \frac{x}{y}\end{aligned}$

Then the slope of the graph at the point (9, 0) will be:

$\displaystyle \begin{aligned} \frac{dy}{dx}\Big|_{(9, 0)} &= \frac{(9)}{(0)} \\ \\ &= \text{Und.}\end{aligned}$

In conclusion, the slope of the graph at the point (9, 0) is undefined.