The mirror image of the parabola $y^2 = 4x$ in the tangent to the parabola at $(1,2)$ $y^2 = 4x$ is?
I have solved this question correctly (by finding the image of the focus and the vertex in the given line and then finding the parabola that possess these parameters) and got the answer to be $(x+1)^2 = 4(y-1)$
In the graph, I have marked all my findings.
I want to know if there's a simpler method to solve this question? But more importantly, what does this reflected parabola signify? It doesn't actually look like a "reflection". For instance, if we find the reflection of any letter with respect to a line mirror, we see that the letter's images are symmetrical about the line but here the parabolas are touching each other and don't look like what we call "reflections". In a nutshell, it contradicts our intuitive sense of "reflection".