examday

/TMUA

The point $P(x_P,y_P)$ lies on the curve $C$ with equation $y^2=4x$, such that $y_P>0$.

Normals are drawn to the curve $C$ at three distinct points, $N_1$, $N_2$, and $N_3$. All three normals pass through the point $P$. Note that one of these points is $P$ itself (i.e., let $N_1=P$).

Let $G$ be the centroid of the triangle formed by the points $N_1$, $N_2$, and $N_3$. Find the set of all possible $x$-coordinates for $G$.