Question

What is the equation of the circle with a center at `(2 ,2 )` and a radius of `4`?

Answer 1

`(x-2)^2 + (y-2)^2 = 16`

Explanation:

Formula for a circle centered on `(h,k)`:

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

`(x-2)^2 + (y-2)^2 = 4^2`

`(x-2)^2 + (y-2)^2 = 16`

graph{(x-2)^2 + (y-2)^2 = 16 [-6.67, 13.33, -3.08, 6.92]}

Answer 2

`(x-2)^2+(y-2)^2=16`

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"`
`"the radius"`

`"here "(a,b)=(2,2)" and r=4`

`(x-2)^2+(y-2)^2=16larrcolor(red)"equation of circle"`