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
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