Write the equation of the circle with center (0,0) and (5,2) a point on the circle

General form of the equation is
(x - a)^2 + (y-b)^2 = r^2

where (a,b)is the center and r = radius
so here we have 
x^2 + y^2 = r^2

Now r^2  =  square  of distance between the points (0,0) and (5,2)

which = (5-0)^2 + (2-0)^2 = 25 + 4 = 29

so the required equation is x^2 + y^2 = 29