83 Passes through the fixed point $M(1,2)$. With the $y$-axis as the directrix, the eccentricity of the ellipse is $\frac{1}{2}$. The equation of the locus of the left vertex of the ellipse is
$839 x^{2}-12 x+4 y^{2}-16 y+19=0$. Let the left vertex be $P(x, y)$, and the left focus be $F\left(x_{1}, y\right)$. Since the eccentricity of the ellipse is $\frac{1}{2}$, the y-axis is the directrix, and it passes through the fixed point $M(1,2)$, we have
$$
\left\{\begin{array}{l}
\frac{x_{1}-x}{x}=\frac{1}{2}, \\
\frac{\sqrt{\left(1-x_{1}\right)^{2}+(2-y)^{2}}}{1}=\frac{1}{2} .
\end{array}\right.
$$

Substituting (1) into (2) yields
$$
9 x^{2}-12 x+4 y^{2}-16 y+19=0 .
$$