Point Contained by a Circle

Date: 8 Aug 1995 19:51:17 -0400
From: Andrew Hartlen
Subject: How can I tell if a point is a circle?

Question: 
        
I did a search on this but didn't find an answer.
I wonder if you could explain to me a formula by which I can
tell whether an arbitrary point on a plane is contained by any arbitrary
circle. And how could you modify this to extend to an ellipse?

Thanks very much,

-a.

Date: 8 Aug 1995 21:25:56 -0400
From: Dr. Ken
Subject: Re: How can I tell if a point is a circle?

Hello there!

The general formula for a circle centered at (m,n) with radius r in the x-y
plane is (x-m)^2 + (y-n)^2 = r^2.  That comes directly from the Pythagorean
Theorem.  Do you see why?  To test whether a given point is on this circle,
you'd simply plug the (x,y) coordinates into that formula and see whether
it's true.  To test whether a given point is on the interior of a circle,
use the formula (x-m)^2 + (y-n)^2 < r^2.  

Similarly, the general formula for an ellipse is a(x-m)^2 + b(y-n)^2 = r^2,
where a and b are greater than zero.  Hope this helps!

-K