A line \(y = mx + c\) intersects the parabola \(y=x^2\) at points \(A\) and \(B\).

The line \(AB\) intersects the y-axis at the point \(P\).

If \(AP-BP=1\) then find \(m^2\).

There are just so many factors to pay attention to, and I don't see any way to use the fact that \(AP-BP=1\) without the distance formula and very complicated square roots. To start though, I listed point A as \((a, a^2) because(y=x^2)\) and B as (\(b, b^2)\), with \(a^2=ma+c\) and \( b^2 = mb+c.\) Point P is also (0, c).

Thanks for any help! From a minor exploit in the "formating tips" section though, this answer should be a fraction, and contain a square root (example: \(\frac{\sqrt2}{5}\))

EnchantedLava68 Jul 13, 2021