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

radius = 4

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