A point Q moves in such a way that the perpendicular distance of Q from the axis of y is equal to the length of the tangent from Q to the circle S. S is the circle

where a is a constant. As you can see the circle has radius 3a/2 and is centred at: (3a/2, 0). We we require the equation of the locus of Q.

So, I decided to define Q as the point

and S a point on the circle as (x, y) since we have the equation of the circle defined in terms of x and y.

We require

call this equation 1 (sorry I don't know how to label equations properly)

So the task is to eliminate

to obtain an equation in x,y and a. I tried:

gives

equating and simplifying gives equation 2: