When asked to find the equation of a tangent line for a function at a particular (c, f(c)) then f(c) doesn't need to be given because it's really just coming from plugging c into f(x) right?

Even though, I'm nearly sure I'm right about this I ask just because it seems strange that this question isn't being asked by only giving you the particular x coordinate.

For example I was asked to find the equation of the tangent line for f(x) = x^2 at the point (2,4). But the question could have just asked find the equation of the tangent line for f(x) = x^2 when x is 2?