Answer
Refer to the graph below.
Work Step by Step
Group the terms with the variable $x$:
$(x^2+6x)+y^2=16$
Complete the square by adding $9$ to both sides:
$(x^2+6x+9)+y^2=16+9
\\(x+3)^2+y^2=25$
This means that the given equation is equivalent to the equation above.
Recall:
The graph of the equation $(x-h)^2+(y-k)^2=r^2$ is a circle whose center is at $(h, k)$ and whose radius is $r$ units.
The equation above can be written as:
$[x-(-3)]^2+(y-0)^2=5^2$
Thus, its graph is a circle whose center is at $(-3, 0)$. with a radius that is 5 units long.
To graph the given equation, perform the following steps:
(1) Plot the following points:
center: $(-3, 0)$
point above the center: $(-3, 0+5)=(-3, 5)$
point below the center: $(-3, 0-5)=(-3, -5)$
point to the left of the center: $(-3-5, 0) = (-8, 0)$
point to the right of the center: $(-3+5, 0) = (2, 0)$
(2) Connect the points (excluding the center) using a smooth curve to form a circle.
Refer to the graph in the answer part above.
