Let $$C$$ be the locus of the mirror image of a point on the parabola $$y^2 = 4x$$ with respect to the line $$y = x$$. Then the equation of tangent to $$C$$ at $$P(2, 1)$$ is:

The parabola is $$y^2 = 4x$$. The mirror image of this curve with respect to the line $$y = x$$ is obtained by interchanging $$x$$ and $$y$$, giving $$x^2 = 4y$$. This is the curve $$C$$.

To find the tangent to $$C: x^2 = 4y$$ at $$P(2, 1)$$, we differentiate implicitly: $$2x = 4\frac{dy}{dx}$$, so $$\frac{dy}{dx} = \frac{x}{2}$$. At $$(2, 1)$$, the slope is $$\frac{2}{2} = 1$$.

The equation of the tangent is $$y - 1 = 1(x - 2)$$, which simplifies to $$x - y = 1$$.