$\begin{array}{ll}
\frac{x_1+0}{2}=h & \frac{y_1+b}{2}=k \\
\Rightarrow x_1=2 h & \Rightarrow y_1=2 k-b
\end{array}$
$\frac{x_1^2}{a^2}+\frac{y_1^2}{b^2}=1 \Rightarrow \frac{4 h^2}{a^2}+\frac{(2 k-b)^2}{b^2}=1 \Rightarrow \frac{h^2}{a^2 / 4}+\frac{\left(k-\frac{b}{2}\right)^2}{b^2 / 4}=1$
$\therefore \frac{x^2}{a^2 / 4}+\frac{\left(y-\frac{b}{2}\right)^2}{b^2 / 4}=1 \rightarrow$ Locus of midpoint which is an ellipse