locus continued (urgent help required before i go insane)

hi guys
thanks so much for the reply but i think i am meant to work it out using the distance formula.

I was thinking of letting P(x,y) being a point on the circle such that x=sqrt16-y^2 and y=sqrt16-x^2

and M being the midpoint (x,y)

I also chose A to be the point on the circle (4,0)

I tried to equate the two so that PA=2MA thus PA^2 = 4MA^2
but then i get in to a mess and can't seem to get the required answer of
x^2 +y^2 - 4x=0

- Hope you can help, it is sending me crazy!!!!!!!!!!!!!!!!!!!!

Please post your reply within the original thread, so people have any idea what you're talking about. Thank you.

Eliz.

The way TKH did the problem is fine.
I would have done differently.
Suppose that B(p,q) is the other end of the cord AB.
Then the midpoint M([p+4]/2 , q/2).
We know that B is on the circle so p<SUP>2</SUP>+q<SUP>2</SUP>=16.
So the locus of M is x=[p+4]/2 or 2x-4=p and likewise 2y=q.
Thus from p<SUP>2</SUP>+q<SUP>2</SUP>=16 we get [2x-4]<SUP>2</SUP>+[2y]<SUP>2</SUP>=16.
This gives us x<SUP>2</SUP>-4x+y<SUP>2</SUP>=0.

Mine used a little more "sleight of hand".

I like yours better. I just wasn't seeing the simpler attack.