Respuesta :

Answer:

center of circle is (3, -7) and the radius is 8

center of circle is (-4,-4) and the radius is [tex]5.66[/tex]

Step-by-step explanation:

[tex]x^{2} +y^{2} -6x +14y-6=0[/tex]

Rearrange the terms

[tex]x^{2} -6x +y^{2} +14y-6=0[/tex]

Using the completing the square method

[tex](x-\frac{6}{2} )^{2} - (\frac{6}{2})^{2} + (y+\frac{14}{2} )^{2} - (\frac{14}{2})^{2} -6 =0[/tex]

Simplify,

[tex](x-\frac{6}{2} )^{2} + (y+\frac{14}{2} )^{2} =64[/tex]

[tex](x-3 )^{2} + (y+7 )^{2} =8^{2}[/tex]

Therefore the center of circle is (3, -7) and the radius is 8

Next example,

[tex]x^{2} +y^{2}+8x+8y=0[/tex]

Rearrange the terms,

[tex]x^{2} +8x+y^{2}+8y=0[/tex]

Using completing the square method,

[tex](x+\frac{8}{2} )^{2} - (\frac{8}{2})^{2} + (y+\frac{8}{2} )^{2} - (\frac{8}{2})^{2} =0[/tex]

Simplify,

[tex](x+4 )^{2} -16 + (y+4)^{2} -16 =0[/tex]

[tex](x+4 )^{2} + (y+4)^{2}= (4\sqrt{2})^{2}[/tex]

Therefore the center of circle is (-4,-4) and the radius is [tex]4\sqrt{2} =5.66[/tex]