The discussion revolves around finding the center and radius of a circle defined by the equation x²+y²-4x+2y+6=0, which falls under the subject area of analytic geometry. Participants explore the implications of the equation, particularly the assertion that the radius squared equals -1, indicating a potential issue with the circle's definition.
The discussion is active, with participants offering guidance on completing the square and questioning assumptions about the equation's implications. There is a mix of attempts to clarify the method and some participants expressing a preference for understanding the process rather than relying on memorized formulas.
Some participants note that the equation can be expressed in a different form involving parameters f and g, but there is disagreement on the effectiveness of this approach compared to completing the square. The original poster expresses confusion about how to derive the conclusion that r² = -1.
Dick said:You complete the squares so you can write it in the form (x+a)^2+(y+b)^2=c. Do you know how to do that?
Dick said:Take the x part. You've got x^2-4x. If I add something to that it will become a perfect square of the form (x-a)^2. What's 'a'? What do you have to add?
Dick said:No, no. (x-a)^2=x^2-2ax+a^2, yes? If you match that up with x^2-4x, the 4 must be the 2a, as I see it. Think back to when you did this before.
kLownn said:Ohh, I see now.. so I just do the same thing for y?
Dick said:Sure.
kLownn said:Homework Statement
Find the centre and radius of the circle x²+y²-4x+2y+6=0
I have the solution. The circle is no defined because r² = -1 is impossible.
But... how do I even DO that equation to get the answer -1?!
No, it isn't. It is much better to actually do the "complete the square" rather than memorize formulas: so you don't make silly mistakes like that.icystrike said:it can actually be express as x²+y²+2fx+2gy+c=0
whrby C(-f,-g) and radius is [tex]\sqrt{g²+f²-c}[/tex]
HallsofIvy said:No, it isn't. It is much better to actually do the "complete the square" rather than memorize formulas: so you don't make silly mistakes like that.