Question 810677
If both x-intercepts are b distance from the Origin, then looking at a picture or graph of this circle should show that the center is on the y-axis.  Can you identify an isosceles triangle? 


The center is some point, (0, c), and since you have a variable for radius, you may have a circle, {{{(x^2)+(y-c)^2=a^2}}}.  We really do not know if c is positive or if c is negative.  We should try to obtain an equation in terms of b, but not with the variable c.


We know two points which are on the circle are (-b,0) and (b,0).
Either one, x^2 will be positive.
Use the point(s) in the equation:  {{{b^2+(0-c)^2=a^2}}}
{{{b^2+c^2=a^2}}}
{{{c^2=a^2-b^2}}}
{{{c=sqrt(a^2-b^2)}}}, using the positive square root just to be simple.


Putting this c into the equation,
{{{highlight(x^2+(y-sqrt(a^2-b^2))^2=a^2)}}}