Question

find all points on the curve y=x^2-2x+4 for which the tangent line passes through the point (1,-1)

Answer 1

detemine the slope of the line at some point (a , b)

y' = 2x - 2, the slope at x=a is simply 2a-2

y* = (2a-2)(x-a) + (b)

y* = (2a-2)(x-a) + (a^2-2a+4) will have to work for the point (1,-1)

-1 = (2a-2)(1-a) + (a^2-2a+4) , solve for a