Question

How do you find the center and radius of the circle `x^2+y^2-2x+6y-26=0`?

Answer 1

`"centre "=(1,-3)" radius "=6`

Explanation:

`"the equation of a circle in standard form is"`

`color(red)(bar(ul(|color(white)(2/2)color(black)((x-a)^2+(y-b)^2=r^2)color(white)(2/2)|)))`

`"where "(a,b)" are the coordinates of the centre and r"`
`"is the radius"`

`"to obtain this form "color(blue)"complete the square"`
`"on both the x and y terms"`

`x^2-2x+y^2+6y=26`

`x^2+2(-1)xcolor(red)(+1)+y^2+2(3)ycolor(magenta)(+9)=26color(red)(+1)color(magenta)(+9)`

`(x-1)^2+(y+3)^2=36larrcolor(blue)"in standard form"`

`"with centre "=(1,-3)" radius "=sqrt36=6`
graph{((x-1)^2+(y+3)^2-36)=0 [-20, 20, -10, 10]}