# Approximation for the equation of an imperfect circle

Given two random points $$(x_0,y_0)$$ and $$(x_1,0)$$ and some condition, I have an equation $$C[(x-x_0)^2+(y-y_0)^2]=[(x-x_1)^2+y^2]^2$$ which is a perfect circle if I ignore the power (2) on the RHS. However, considering the power on the RHS, which makes it an imperfect circle, I aim to apply some approximation so that I can obtain the equation of a circle i.e. $$(x-A)^2+(y-B)^2=r^2$$

Just for the illustration, I have taken some random points and plotted the above equation in Mathematica, which gives me an imperfect circle as expected

• Approximate center and radius analytically? Isn't that kind of contradiction? – Dair Apr 12 at 1:51
• OK. The center is $(0,0)$ and the radius is $14$. That's a very bad approximation most of the time, but without a criterion for success, it's about as good as any other. Can you perhaps spend a little time refining your question so that we (and you) both know the goal we're working toward? – John Hughes Apr 12 at 2:04
• For the reason John Hughes explained, I'd voted to close this question as unclear. – Travis Apr 12 at 2:21
• @RabeArshad if you ignore the power 2 on the RHS you get a line instead, not a circle. – user10354138 Apr 12 at 2:38
• I think the question is pretty clear. Just not completely specified, which, IMHO, is okay. – Jair Taylor Apr 12 at 3:02