Locus

Explanation as follows:

圖片參考：http://i238.photobucket.com/albums/ff245/chocolate328154/Maths470.jpg?t=1221126532


2008-09-11 18:33:58 補充：
我好肯定eelyw個答案係錯!!!
因為個y - intercept 係5 => ( 0 , 5 ) is a pt on the circle, so sub x = 0, y = 5
L.H.S. = (0 - 3)^2 + [5 - (sqrt 61)/2]^2
= 10.199
R.H.S. = 61 / 4
= 15.25
=/= L.H.S.

Let radius of circle = r. Therefore, centre of circle is at (3,r). So equation of circle is
(x - 3)^2 + (y -r)^2 = r^2
Since the circle intersects the y - axis, that is x = 0, we put x = 0 and get
9+ y^2 + r^2 - 2ry - r^2 = 0
y^2 - 2ry + 9 = 0.
Let the 2 roots of the equation be h and k, therefore,
h + k = 2r............(1) and
hk = 9...............(2)
So (h - k)^2 = h^2 + k^2 - 2hk = (h + k)^2 - 4hk = 5^2 = 25
4r^2 - 36 = 25
r^2 = 61/4, r = (sqrt61)/2
So equation of circle is
(x - 3)^2 + [y - (sqrt 61)/2]^2 = 61/4.