Question

#9 find an equation of the circle with radius 6 & center (1, -5)

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.

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

Given that the center is $(1,-5)$, so $h = 1$, $k=-5$. And the radius $r = 6$.

Step3: Substitute values into the formula

Substitute $h = 1$, $k=-5$, and $r = 6$ into the equation $(x - h)^2+(y - k)^2=r^2$. We get $(x - 1)^2+(y+5)^2=36$.

Answer:

$(x - 1)^2+(y + 5)^2=36$