I am rather depressed that I can't get this one. Attached is a diagram to go with the following question:
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.
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:
equating and simplifying gives equation 2:
Find grad of circle S by implicit differentiation:
So grad =
Now you would think that this and equations 1 and 2 would enable me to eliminate the subscript terms. Instead I am getting masses of terms that don't simplify to anything. A sure sign I am off base. So, can anyone help?