Question

find an equation for the circle. center at (- 10,0), radius 2. a. $x^{2}+(y - 10)^{2}=2$ b. $(x + 10)^{2}+y^{2}=4$ c. $(x - 10)^{2}+y^{2}=4$ d. $x^{2}+(y + 10)^{2}=2$

Explanation:

Step1: Recall the standard - form of a circle equation

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

Step2: Identify the values of $h$, $k$, and $r$

Given that the center is $(- 10,0)$ and radius $r = 2$. So, $h=-10$, $k = 0$, and $r = 2$.

Step3: Substitute the values into the standard - form

Substitute $h=-10$, $k = 0$, and $r = 2$ into $(x - h)^2+(y - k)^2=r^2$. We get $(x-(-10))^2+(y - 0)^2=2^2$, which simplifies to $(x + 10)^2+y^2=4$.

Answer:

B. $(x + 10)^2+y^2=4$