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Find the value of m > 0 for which the line y = mx touches the parabola y = (x - 1)^{2}+ 1 at just one point.

So far what I've done...

I know that if the line touches the parabola at one point, it is tangential. So I put together the 2 equations in order to find the intersection (or touch):

mx=(x-1)^{2}+1

0=x^{2}-2x-mx+2

0=x^{2}-(2+m)x+2

That's as far as I've gotten. Someone said I need to find the restriction on 'm' so that the equation only has one root (just touches, as opposed to a full intersection through 2 points), but I don't know what to do...

Any help would be appreciated.

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# Homework Help: Value of when a line touches a parabola at one point.

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