Question

a circle has the equation 2(x - 2)² + 2y² = 2.
(a) find the center (h,k) and radius r of the circle.
(b) graph the circle:
(c) find the intercepts, if any, of the graph.

(a) the center of the circle is (2,0).
(type an ordered pair, using integers or decimals.)
the radius of the circle is 1.
(type an integer or a decimal.)
(b) use the graphing tool to graph the circle.
(c) what are the intercepts? select the correct choice below and, if necessary, fill in the answer box within your choice.
a. the intercept(s) is/are (1,0)∪(3,0).
(type an ordered pair. use a comma to separate answers as needed. type exact answers for each coordinate, using radicals as needed.)
b. there are no intercepts.

Explanation:

Step1: Simplify circle equation

Divide by 2: $(x-2)^2 + y^2 = 1$
Standard form: $(x-h)^2 + (y-k)^2 = r^2$
Center $(h,k)=(2,0)$, radius $r=1$

Step2: Find x-intercepts (y=0)

Substitute $y=0$: $(x-2)^2 + 0 =1$
$(x-2)^2=1$ → $x-2=±1$ → $x=3$ or $x=1$
Intercepts: $(1,0),(3,0)$

Step3: Find y-intercepts (x=0)

Substitute $x=0$: $(0-2)^2 + y^2=1$ → $4+y^2=1$ → $y^2=-3$ (no real solutions)

Answer:

(a) Center: (2,0); Radius: 1
(b) Graph centered at (2,0) with radius 1 (matches the provided graph)
(c) A. The intercept(s) is/are (1,0),(3,0)