Question

Graph the circle (x+6)^2 + (y+5)^2 =9

Answer 1

This a circle centered at the point
`(-6,-5)`, and of radius "3" as it is shown in the attached image.

Explanation:

Recall that the standard formula for a circle of radius "R", and centered at the point
`(x_0,y_0)` is given by:

`(x-x_0)^2+(y-y_0)^2=R^2`

Therefore, in our case, by looking at the standard equation they give us, we extract the following info:

1)
`R^2 = 9\,\,\,then\,\,\,R=3` since the radius must be a positive number and (
`R=-3`) is not a viable answer.

2)
`x_0=-6` for (
`x-x_0`) to equal
`(x+6)`

3)
`y_0=-5` for (
`y-y_0`) to equal
`(y+5)`

Therefore, we are in the presence of a circle centered at the point
`(-6,-5)`, and of radius "3". That is what we draw as seen in the attached image.