Question

select the correct answer.
which equation represents circle n?
l(-2,11)
n(-7,6)
a. ((x + 7)^2 + (y - 6)^2 = 25)
b. ((x - 7)^2 + (y + 6)^2 = 25)
c. ((x + 7)^2 + (y - 6)^2 = 50)
d. ((x - 7)^2 + (y + 6)^2 = 50)

Explanation:

Step1: Recall circle equation form

The standard equation of a circle is $(x-h)^2+(y-k)^2=r^2$, where $(h,k)$ is the center, and $r$ is the radius.

Step2: Identify center coordinates

Center $N$ is $(-7,6)$, so $h=-7$, $k=6$. Substitute into the equation:
$(x-(-7))^2+(y-6)^2=r^2$ which simplifies to $(x+7)^2+(y-6)^2=r^2$

Step3: Calculate radius squared

Use point $L(-2,11)$ on the circle. Compute $r^2$ using distance formula:
$r^2=(-2 - (-7))^2+(11-6)^2$
$r^2=(5)^2+(5)^2=25+25=50$

Step4: Substitute $r^2$ into equation

$(x+7)^2+(y-6)^2=50$

Answer:

C. $(x + 7)^2 + (y - 6)^2 = 50$