The curve C1: y = x ^ 2yu and C2: y = - (X-2) ^ 2, the line L and C1C2 are tangent, find the equation of the line L. use the derivative function of two curves to find out why it can't be used | Math enthusiast | Mathematical art

The curve C1: y = x ^ 2yu and C2: y = - (X-2) ^ 2, the line L and C1C2 are tangent, find the equation of the line L. use the derivative function of two curves to find out why it can't be used

Let the linear equation be y = ax + B, and the line intersects with the curve C1 at the point (m, m ^ 2). Compared with the curve C2 at the point (n, - n ^ 2 + 4n-4), y '= 2x can be obtained by y = x ^ 2. For the same reason, y' = - 2x + 4 can be obtained by y = - (X-2) ^ 2

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