Name the quadrant in which the graph of point $P\left(x, y\right)$ lies when $x>0$ and $y>0$.

In the adjoining figure, $PQR$ is an equilateral triangle in which coordinates of $Q$ and $R$ are $\left(0, 4\right)$ and $\left(0, -4\right)$, respectively. Find the coordinates of the vertex $P$.