How do I find the tangent of the acute angle at which the parabolas y =x^2 and y = (x-2)^2 intersect.
Thanx a lot!
Well the parabolas obviously intersect at (1,1). However, I am not at all sure what you mean by the phrase "tangent of the actute angle". It should be easy enough to find the equation of each parabola's tangent at the point of intersection, and then you can easily find the acute angle between those two lines (e.g. by computing the dot and/or cross product between unit vectors along those two tangents). And then it should be easy enough to find the equation of the line which you might interpret as a "tangent" to the angle - i.e the bisector of the obtuse angle.