Can we find the area of the triangle created by a common tangent?

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Prove that the curves \(y^2 = 16x\) and \(y = x^2 + 3\) touch at the point \((1,4)\).

The important word here is touch.

Suppose two curves both go though a point \(P\). What can we say about the tangent to each curve at \(P\) if the curves touch at \(P\)?