Ellipse

$L_1^{\prime}$ is the end of a latus rectum of the ellipse $3x=2 \pm \frac{\sqrt{5}}{\sqrt{5}}$ $3 x^2+4 y^2=12$ which is lying in the third quadrant. If the normal drawn at $L_1^{\prime}$ to this ellipse intersects the ellipse again at the point $P(a, b)$, then $a=$