If

*m* is the slope of the curve $\displaystyle xy=3$ and m

2 is the slope of the curve $\displaystyle x^2-y^2=4$, then at a point of intersection of the two curves:

- (A) m1 = m2
- (B) m1= -m2
- (C) m1*m2 = 1
- (D) m1*m2 = -1
- (E) m1*m2 = -2

I think I might be doing it wrong... >_<

First, I found the derivative of the first one explicitly.

$\displaystyle

\frac{dy}{dx}[3x^-1]

$

which is:

$\displaystyle

\frac{-3}{x^2}

$

And then, the derivative of the second one implicitly:

$\displaystyle

\frac{dy}{dx}[x^2-y^2]=\frac{dy}{dx} [4]$

which is:

$\displaystyle

\frac{dy}{dx}= \frac{x}{y}$

But I can't see a relationship between the two slopes...?