Re: Math Problem


PaulHjelmstad wrote:
> This is one that a piano student of mine was working on.
> She apparently solved it, but I don't get it.
>
> Given the parabola y=x^2, find two lines perpendicular to one another that are both tangent to this parabola.
>
> (The tangent lines must have slope y=|2x|, right?

2x

The slope of y = x^2 is negative on the left of the y-axis.

> And perpendicular lines are nx, -(x/n) right? So I don't see
> how this problem could have any solutions

Any x1, x2 such that (2x1)(2x2) = -1 will constitute a solution.

For instance x1 = 1, x2 = -1/4. The tangent at x = 1 is the line
y = 2x -1, with slope 2. The tangent at x2 = -1/4 is the line
16y + 8x = -1, with slope -1/2.

- Randy

.

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