Respuesta :

you can do this by completing the square on x and y terms:

  x^ - 10x + y^2 + 6y + 18 = 0

  (x - 5)^2 -25 + (y + 3)^2 - 9 + 18 = 0

  (x - 5)^2  + (y + 3)^2 = -18 + 9 + 25  =  16


so radius = sqrt16  = 4 answer

Answer:

radius = 4

Step-by-step explanation:

the radius of a circle whose equation is [tex]x^2 + y^2 - 10x + 6y + 18 = 0[/tex]

write the equation in center radius form

[tex](x-h)^2+(y-k)^2= r^2[/tex]

Use completing the square method, take the coefficient of x  and y . then divide it by 2 and then square it. Add it on both sides

[tex]x^2- 10x+ y^2 + 6y + 18 = 0[/tex]

[tex](x^2- 10x+25)+ (y^2 + 6y+9) + 18 = 25+9[/tex]

[tex](x-5)^2+ (y+3)^2 + 18 = 25+9[/tex]

Subtract 18 on both sides

[tex](x-5)^2+ (y+3)^2=16[/tex]

radius [tex]r^2=16[/tex]

Take square root on both sides

radius r= 4

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