Question

What is the equation of a circle with its center at (-6, -3) and a radius of 12?

Answer 1

The general formula for a circle with center `(a,b)` and radius `r` is `(x-a)^2+(y-b)^2=r^2` so substituting we get

`(x+6)^2 + (y+3)^2= 144`

Answer 2

`(x+6)^2+(y+3)^2=144`

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"`

`"here "a=-6,b=-3" and "r=12`

`"substitute these values into the equation"`

`(x-(-6))^2+(y-(-3))^2=12^2`

`rArr(x+6)^2+(y+3)^2=144larrcolor(red)"equation of circle"`