i have solved this for my tutor before but i can't find my solutions..

but i think, this can be solved in two ways, one is using calculus while the other is using some college algebra..

let (0,k), k>0 be the center of the circle:

let us use the fact that both are symmetric wrt to y axis.. hence, let (a,b) and (-a,b) be the points of intersection..

so,

and

and so if we combine both, we have

or

using quadratic formula, we have:

for that to exists, we need

or

in fact, what we need is that

so that we have a unique solution for

and that

*a* has 2 solutions.. Ü so if

, we have

or

. and

hence, the points are

and

EDIT: i hang up to eat; and then, jhevon had answered it already.. hehe