Thread: Circles with radius 0?

What does the equation x^2+y^2=0 represent?

Is it a circle of radius 0? I don't think it is because that really doesn't make sense. Wouldn't it just be the degenerate conic of a point? (i.e. the point (0,0))

Originally Posted by twittytwitter

What does the equation x^2+y^2=0 represent?

Is it a circle of radius 0? I don't think it is because that really doesn't make sense. Wouldn't it just be the degenerate conic of a point? (i.e. the point (0,0))

Yes it's just the point (0, 0).

There are a few ways you can think about it. I would probably do this...



The LHS is nonnegative, the RHS is nonpositive. So that means the only way for the equation to be satisfied is for both sides to be equal to 0.

But it is, strictly speaking, incorrect to talk about a "circle with radius 0". It is perfectly valid to call it a "degenerate conic section".

Originally Posted by HallsofIvy

But it is, strictly speaking, incorrect to talk about a "circle with radius 0". It is perfectly valid to call it a "degenerate conic section".

Why not a "degenerate circle"?