A circle passes through the points A, B, and C which have coordinates respectively.

Equation of circle

A line y=mx-3of variable gradient m, cuts the circle at L and M. Find the Cartesian equation of the locus of the midpoint of the line LM.

I found the values of x and y in terms of m.

Now what's next? I don't know hot to proceed from here. Any help is greatly appreciated! Thanks!