Originally Posted by

**joatmon** Yeah, I thought of that (and probably should have listed it in my original post), but I still don't know how to integrate it into this solution. Here's some further thoughts:

Let $\displaystyle L_1$ = the positively sloping line and $\displaystyle L_2$ be the negatively sloping line.

Let $\displaystyle L_1$ pass through the points, $\displaystyle (x_1, y_1)$ and $\displaystyle (0, y_2)$ where $\displaystyle y_2 < 0$.

Since $\displaystyle y = 9x^2$ is even, this means that $\displaystyle L_2$ passes through $\displaystyle (-x_1, y_1)$ and $\displaystyle (0, y_2)$.

As you point out, the slopes are negative reciprocals of each other, by definition.

Then, there are a couple of things that I think are true, but I don't know just how to prove them. First $\displaystyle m_1 = 1$ and $\displaystyle m_2 = -1$. I say this because, in order to be tangent to an even function, the only way that I can see two perpendicular lines meeting at the y-axis would be if they both had symmetrical x-coordinates (e.g. (5, 0) and (-5, 0)).

If that is true, this final one might be the key to the whole thing. If the slope is 1 or -1, and the lines intersect at the y-axis, then doesn't $\displaystyle y_2$ have to equal $\displaystyle -(y_1)$?

Am I on the right track? Making this to complicated? Any help is appreciated.

Thanks again.