How do you solve a circle equation without having the radius
Ex. R ^2= (5-h)^2+(5-k)^2 ?

What do you want to get as an answer? What does it mean to solve a circle euqation to you? How many variables do you have in this "circle" equation?

A circle equation is (x-h)^{2}+(y-k)^{2}=r^{2}

Where (h,k) is the coordinates of the center and (x,y) is a point on the circle.

In your case, (x,y)=(5,5), a point on the circle. That's about it. What is it you want to solve?

We have no center coordinates nor radius. The way it is there are a infinite number of circles that could meet that.

What is required by you in the answer is not clear.

What do you want to get as an answer? What does it mean to solve a circle euqation to you? How many variables do you have in this "circle" equation?

How do I find centre of circle? When equation=(x-1)^2+(y-k)^2=10, and circle co-ordinates (2,5)

abelle, have to taken notice of galactus' post (https://www.askmehelpdesk.com/mathematics/how-solve-circle-equation-303868.html#post1489829) a little above?

There are all the explanations for your problem there.

You have a point on the circle, (2, 5).

Find 'k' the y-coordinate of the circle that you don't have. You already have the x-coordinate of the centre of circle as 1 here.