Question

find an equation of the circle centered at (x, y) = (-1, 6) with a radius of r = 9 units.

Explanation:

Step1: Recall circle - equation formula

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

Step2: Identify the values of $a$, $b$, and $r$

Given that the center is $(a,b)=(-1,6)$ and $r = 9$. Here $a=-1$, $b = 6$, and $r=9$.

Step3: Substitute the values into the formula

Substitute $a=-1$, $b = 6$, and $r = 9$ into $(x - a)^2+(y - b)^2=r^2$. We get $(x-(-1))^2+(y - 6)^2=9^2$.

Step4: Simplify the equation

$(x + 1)^2+(y - 6)^2=81$.

Answer:

$(x + 1)^2+(y - 6)^2=81$