Locus of the mid-points of the intercepts between the coordinate axes by the lines passing through  $(a, 0)$ does not intersect

Equation of any line through $(a, 0)$ be $\frac{x}{a}+\frac{y}{b}=1$ where $b$ is a parameter. This line meets $y-axis$ t $(0, b)$ and if $(h, k)$ denotes the mid-point of the intercept of the line between the coordinate  axes, then $h=a / 2, k=$ $b / 2$ and then the locus of $(h,k)\text{ is }x=a/2$. This clearly does  not intersect $y-axis$.