If the tangents drawn from the point $\left(0,2\right)$ to the parabola $y^2=4ax$ are inclined at an angle of $\frac{3\pi }{4}$ then the value of $a$ is:

Let there be two parabolas with the same axis, focus of each being exterior to the other and the latus rectum being $4a$ and $4b$. The locus of the middle points of the intercepts between the parabolas made on the lines parallel to the common axis is a