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

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

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

Answer

Explanation:

Step1: Recall circle - equation formula

The standard form of the equation of a circle is $(x - h)^2+(y - k)^2=r^2$, where $(h,k)$ is the center of the circle and $r$ is the radius. The center of circle $N$ is $N(-7,6)$, so $h=-7$ and $k = 6$. The equation of the circle becomes $(x+7)^2+(y - 6)^2=r^2$.

Step2: Calculate the radius

The radius $r$ is the distance between the center $N(-7,6)$ and a point on the circle $L(-2,11)$. Use the distance formula $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $x_1=-7,y_1 = 6,x_2=-2,y_2 = 11$. Then $r=\sqrt{(-2+7)^2+(11 - 6)^2}=\sqrt{5^2+5^2}=\sqrt{25 + 25}=\sqrt{50}$. So $r^2 = 50$.

Answer:

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