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Finding the center and radius by completing the square
4x(sqrd)+4y(sqrd)+4x-16y-19=0

Sagot :

naǫ
[tex](x-h)^2+(y-k)^2=r^2[/tex]
(h,k) - the center
r - the radius

[tex]4x^2+4y^2+4x-16y-19=0 \ \ \ |\div 4 \\ x^2+y^2+x-4y-\frac{19}{4}=0 \\ x^2+x+\frac{1}{4}+y^2-4y+4-\frac{19}{4}-\frac{1}{4}-4=0 \\ (x+\frac{1}{2})^2+(y-2)^2-\frac{20}{4}-4=0 \\ (x+\frac{1}{2})^2+(y-2)^2-5-4=0 \\ (x+\frac{1}{2})^2+(y-2)^2-9=0 \\ (x+\frac{1}{2})^2+(y-2)^2=9 \\ (x+\frac{1}{2})^2+(y-2)^2=3^2[/tex]

The center - [tex](-\frac{1}{2},2)[/tex]
The radius - [tex]3[/tex]
konrad509
[tex] 4x^2+4y^2+4x-16y-19=0 \\ 4x^2+4x+1+4y^2-16y+16-36=0\\ (2x+1)^2+(2y-4)^2=36[/tex]

center - [tex](-1,4)\\ [/tex]
[tex]r=\sqrt{36}=6[/tex]
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