Question

What is the radius of a circle whose equation is x2 + y2 – 10x + 6y + 18 = 0?

Answer 1

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 2

Answer:

radius = 4

Step-by-step explanation:

the radius of a circle whose equation is $x^2 + y^2 - 10x + 6y + 18 = 0$

write the equation in center radius form

$(x-h)^2+(y-k)^2= r^2$

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

$x^2- 10x+ y^2 + 6y + 18 = 0$

$(x^2- 10x+25)+ (y^2 + 6y+9) + 18 = 25+9$

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

Subtract 18 on both sides

$(x-5)^2+ (y+3)^2=16$

radius $r^2=16$

Take square root on both sides

radius r= 4