Point Contained by a CircleDate: 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 |
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