Question

How do you find the center and radius of the circle `x^2 + y^2 - 6x + 8y = 0`?

Answer 1

`"centre "=(3,-4)" and radius "=5`

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"`

`"use the method of "color(blue)"completing the square"`
`"on both the x and y terms"`

`x^2-6x+y^2+8y=0`

`x^2+2(-3)x color(red)(+9)+y^2+2(4)y color(magenta)(+16)=0color(red)(+9)color(magenta)(+16)`

`(x-3)^2+(y+4)^2=25larrcolor(blue)"in standard form"`

`"centre "=(3,-4)" and radius "=sqrt25=5`