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True/False: A graph that contains just a single point (h,k) can be written as (xh)^2+(yk)^2=0 which means it can be seen as a circle with radius 0.
Please state what you think. Don't look it up on a website because I can do that if that is what I wanted. :)
 one year ago
 one year ago
True/False: A graph that contains just a single point (h,k) can be written as (xh)^2+(yk)^2=0 which means it can be seen as a circle with radius 0. Please state what you think. Don't look it up on a website because I can do that if that is what I wanted. :)
 one year ago
 one year ago

This Question is Closed

ilikephysics2Best ResponseYou've already chosen the best response.0
Its true...i didnt look it up
 one year ago

myininayaBest ResponseYou've already chosen the best response.0
That is what I say to but people actually do take the other side on this one. If there is any reason why you think it is true, can you say why?
 one year ago

ilikephysics2Best ResponseYou've already chosen the best response.0
that is the formula for it , look in your book
 one year ago

experimentXBest ResponseYou've already chosen the best response.2
the equality only hold for (x,y) = (h,k) for any set of point other than (h, k) this relation is not valid in Real plane.
 one year ago

ilikephysics2Best ResponseYou've already chosen the best response.0
@experimentX its the formula for it man
 one year ago

experimentXBest ResponseYou've already chosen the best response.2
formula is just expression of logic.
 one year ago

CliffSedgeBest ResponseYou've already chosen the best response.1
Some people don't like the idea of calling something with zero size a circle (or any other plane figure), but I don't have a problem with it. If you want to be more precise, it's the limit of a circle as its radius approaches zero.
 one year ago

CliffSedgeBest ResponseYou've already chosen the best response.1
That is the standard form of an equation for a circle with r=0, so why not? I would be more general and say it's an ellipse of size zero, but I'm a dork like that.
 one year ago

myininayaBest ResponseYou've already chosen the best response.0
I think it depends on how you define a circle. I would say the radius could be greater than equal to 0. Someone told me you can actually prove that when you have (xh)^2+(yk)^2=0 this is a circle.
 one year ago

myininayaBest ResponseYou've already chosen the best response.0
I left out the word "or"
 one year ago

CliffSedgeBest ResponseYou've already chosen the best response.1
Depends on if you want a synthetic geometry definition, analytic geometry definition, calculus definition. As far as I'm concerned, It is a circle. It's a circle with r=0.
 one year ago

CliffSedgeBest ResponseYou've already chosen the best response.1
So, in more plain language (or using a geometry definition), it would be better to call it a point rather than a circle, but as long as you are clear in your definitions and can show your logic is consistent in either case, either way works.
 one year ago

ZarkonBest ResponseYou've already chosen the best response.2
if you let r=0 then you will destroy properties that all 'normal' circles have
 one year ago

myininayaBest ResponseYou've already chosen the best response.0
You put quotation marks around normal because you do see it as a circle @zarkon , but not a "normal" circle ?
 one year ago

ZarkonBest ResponseYou've already chosen the best response.2
I would call it a degenerate circle
 one year ago

CliffSedgeBest ResponseYou've already chosen the best response.1
I like "degenerate."
 one year ago

CliffSedgeBest ResponseYou've already chosen the best response.1
It's a shorter way of saying "circle with radius zero."
 one year ago

experimentXBest ResponseYou've already chosen the best response.2
perhaps that way we could avoid confusing the difference between these two. (xh)^2+(yk)^2=0 a(xh)^2+b(yk)^2=0
 one year ago

precalBest ResponseYou've already chosen the best response.0
but isn't a circle just defined as a center with all points on the circumference equadistant fro the center. Hmmmmm center and circumference are the same here.......
 one year ago

CliffSedgeBest ResponseYou've already chosen the best response.1
I don't see why the center and circumference cannot coincide. There is nothing in the definition of a circle that forbids that.
 one year ago

ZarkonBest ResponseYou've already chosen the best response.2
that depends on what definition you use
 one year ago

ZarkonBest ResponseYou've already chosen the best response.2
I like my circles to have interiors..and the break the plane into two regions (not including the circle itself)
 one year ago

ZarkonBest ResponseYou've already chosen the best response.2
that way all my theorems hold and make sense
 one year ago

joemath314159Best ResponseYou've already chosen the best response.0
Maybe thinking of the equation as a "circle" is what makes it seem confusing. Think of it as a distance function:\[d: \mathbb{R}^2\times\mathbb{R}^2\rightarrow\mathbb{R}\]\[((x_1,y_1),(x_2,y_2))\longmapsto \sqrt{(x_1x_2)^2+(y_1y_2)^2}\]
 one year ago

joemath314159Best ResponseYou've already chosen the best response.0
Then in a sense, when you have:\[(xh)^2+(yk)^2=0\]you are saying "I want the set of all points (x,y) such that the distance between (x,y) and (h,k) is zero."
 one year ago

CliffSedgeBest ResponseYou've already chosen the best response.1
@joemath314159 the equation of a circle, the distance formula, and the pythagorean theorem are all the same thing.
 one year ago

ZarkonBest ResponseYou've already chosen the best response.2
draw a tangent to a circle with radius zero
 one year ago

CliffSedgeBest ResponseYou've already chosen the best response.1
@Zarkon why does a tangent need to be defined in order for it to be a circle?
 one year ago

ZarkonBest ResponseYou've already chosen the best response.2
all other circles have that property..and many other properties that are destroyed by having r=0...maybe it should have its own name...like "point"
 one year ago

CliffSedgeBest ResponseYou've already chosen the best response.1
And even if there is no single unique tangent to that point, a tangent can still be drawn.
 one year ago

CliffSedgeBest ResponseYou've already chosen the best response.1
Those are properties of some circles, but are they included in the definition of "circle?"
 one year ago

CliffSedgeBest ResponseYou've already chosen the best response.1
Argument from personal preference isn't valid, I'd think.
 one year ago

ZarkonBest ResponseYou've already chosen the best response.2
most are theorems that require that a circle have an interior
 one year ago

CliffSedgeBest ResponseYou've already chosen the best response.1
Then that's just too bad. You use those theorems when they apply. If they don't apply, you don't use the theorems. Whether or not particular theorems apply does not change the definition of "circle."
 one year ago
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