Question

find all parabolae which share the same tangent line at (1,1) as y=x^2

Answer 1

maybe like this: general parabola formula is\[y=ax ^{2}+bx+c\]
the general derivative is y'=2ax+b
at x=1 y=x^2 derivative is y'=2
so parabolas for which 2a+b=2 will have same drivative

Answer 2

thanks!

Answer 3

yw