How do you write the equation of the locus of all points in the coordinate plane 8 units from (4, 10)?
By definition, the locus of all the points who have the same distance from a fixed centre is a circle. So, that was a complex way to ask for a circle of center
If you know the center coordinates
In your case,
You can either leave it as it is, or expand the squares and sum all the coefficients: