Answer
(a)
center: $(0, 0)$
radius = $2$
(b)
Refer to the image below for the graph.
(c)
x-intercepts: $-2$ and $2$
y-intercepts: $-2$ and $2$
Work Step by Step
RECALL:
The standard form of a circle's equation is:
$(x-h)^2 +(y-k)^2=r^2$
where $r$ = radius and $(h, k)$ is the center.
The given equation can be written as: $(x-0)^2+(y-0)^2 = 2^2$
Thus,
(a)
The given circle has:
center: $(h, k)=(0, 0)$
radius = $r=2$
(b)
To graph the circle, perform the following steps:
(1) Plot the center $(0, 0)$.
(2) With a radius of $2$ units, plot the following points:
2 units to the left of the center: $(-2, 0)$
2 units to the right of the center: $(2, 0)$
2 units above the center: $(0, 2)$
2 units below the center: $(0, -2)$
(3) Connect the four points above (not including the center) using a smooth curve to form a circle
(Refer to the attached image in the answer part above for the graph.)
(c)
The graph shows that the circle has the following intercepts:
x-intercepts: $-2$ and $2$
y-intercepts: $-2$ and $2$
