The equation of a circle is x2 + y2 + Cx + Dy = E. If the radius of the circle is decreased without changing the coordinates of the center point, how are the coefficients C, D, and E affected?

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surjithayer · Answer

@surjithayer wrote:

$$x^2+y^2+Cx+Dy=E$$ $$x^2+Cx+(\frac{ C }{ 2 })^2+y^2+Dy+(\frac{ D }{ 2 })^2=E+(\frac{ C }{ 2 })^2+(\frac{ D }{ 2 })^2$$ $$(x+\frac{ C }{ 2 })^2+(y+\frac{ D }{ 2 })^2=(\sqrt{E+\frac{ C^2 }{ 4 }+\frac{ D^2 }{ 4 }})^2$$ center$$=(-\frac{C}{2},-\frac{D}{2})$$ $$radius=\sqrt{E+\frac{ C^2 }{ 4 }+\frac{ D }{ 4 }}$$ as C and D are fixed. so for radius to change only E changes.