SOLUTION: could you help me about this? Derermine the value (or set of values) of K for which the equation x^2+y^2-2x-4y=K represents a real circle, a point, and an imaginary circle. i r

Algebra ->  Equations -> SOLUTION: could you help me about this? Derermine the value (or set of values) of K for which the equation x^2+y^2-2x-4y=K represents a real circle, a point, and an imaginary circle. i r      Log On


   

Question 203605: could you help me about this?
Derermine the value (or set of values) of K for which the equation x^2+y^2-2x-4y=K represents a real circle, a point, and an imaginary circle.
i rewrite the equation to (x-1)^2+(y-2)^2=K-5 but i dont know how should i go on =(
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Derermine the value (or set of values) of K for which the equation x^2+y^2-2x-4y=K represents a real circle, a point, and an imaginary circle.
i rewrite the equation to (x-1)^2+(y-2)^2=K-5 but i dont know how should i go on =(
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If your work is correct up to that point,
K-5 is the square of the radius of the circle.
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If sqrt(K-5) is positive you have a real circle.
If sqrt(K-5) is zero you have a point
If sqrt(K-5) is negative you have an imaginary circle.
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Cheers,
Stan H.