Question

$(x-5)^{2}+(y+7)^{2}=8$
b) sketch the graph of the circle. choose the correct graph
a.
b.
c.
d.
c) determine the x- and y-intercepts of the circle. select the correct choice and, if necessary, fill in the answer box within your choice
a. the x-intercept(s) is/are x =
(use a comma to separate answers as needed. type an exact answer, using radicals as needed )
b. there is no x-intercept

Explanation:

Step1: Recall circle standard form

The standard form of a circle is $(x-h)^2+(y-k)^2=r^2$, where $(h,k)$ is the center and $r$ is the radius. For $(x-5)^2+(y+7)^2=8$, we have $h=5$, $k=-7$, $r=\sqrt{8}=2\sqrt{2}\approx2.83$.

Step2: Verify graph match

A circle with center $(5,-7)$ and radius ~2.83 will be in the fourth quadrant, matching option C.

Step3: Find x-intercepts (set y=0)

Substitute $y=0$ into the equation:
$$(x-5)^2+(0+7)^2=8$$
$$(x-5)^2+49=8$$
$$(x-5)^2=8-49=-41$$
Since a square cannot equal a negative number, there are no real x-intercepts.

Answer:

b) C
c) B. There is no x-intercept