find center of circle from one point,knowing radius

Question

I have a problem that I have to solve. I need to find center of the circle containing the point $(x,y)$. The point is $x=2,y=3$ with radius $r=3$. I need to find the center of circle. Is there equation for that? I use this equation.
$$(x-h)^2+(y-k)^2=r^2$$ How I can find $h$ and $k$ for the center of circle if I know the point on circle and the diameter of circle?

Answer 1

You have one equation in two unknowns, so should not expect a unique solution. Draw a circle around $(2,3)$ with radius $3$. Any of the points on this circle could be the center of the circle you seek.

Answer 2

Acoording to you $(x,y)$ is the centre with radius $3$ . So by the distance formula $(x-2)^2+(y-3)^2=3^2=9$. Then by plugging in any value for y you get a corresponding value for x. There are 2 unknowns and only 1 equation. So we need another parameter to solve for a specific point. Two, of the infinitely many, answers are for example: $(x,y)=(2,6)$ or $(2\sqrt{2},4)$.