Question

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

Answer 1

Answer:

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

Step-by-step 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.