Question

Graph the circle which is centered at (4,4) and has a radius of 3 units.

Answer 1

Please refer to attached image for the graph of required circle.

Explanation:

The center and radius equation of a circle is :

`(x-h)^2 + (y-k)^2 = (r)^2 ...... (1)`

Where the co-ordinates
`(x,y)` from where the circle passes.

`(h,k)` is the co-ordinate of circle's center represented by O.

`r` is the radius of circle.

Here, we are given that center of circle is at
`(4,4)`.

So,
`h = 4\ and\ k = 4`.

and
`r = 3`

Hence, the equation (1) can be represented as :

`\Rightarrow \left(x-4\right)^(2)+\left(y-4\right)^(2)=3^(2)\\\Rightarrow \left(x-4\right)^(2)+\left(y-4\right)^(2)=9`

Please refer to the image attached in the answer area for the graph of above equation of circle.

Center of circle is represented by O which is the co-ordinate (4,4).

(7,4) is another point on circle.

The radius of circle is also shown in the graph image attached.