Question

1. choose the equation of a circle with radius 6 and center (3, -5). (a) (x - 3)^2 + (y + 5)^2 = 6 (b) (x + 3)^2 + (y - 5)^2 = 36 (c) (x + 3)^2 + (y - 5)^2 = 6 (d) (x - 3)^2 + (y + 5)^2 = 36

Explanation:

Step1: Recall circle - equation formula

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 values of $h$, $k$, and $r$

Given center $(3,-5)$ and radius $r = 6$. Here $h = 3$, $k=-5$.

Step3: Substitute values into the formula

Substitute $h = 3$, $k=-5$, and $r = 6$ into $(x - h)^2+(y - k)^2=r^2$. We get $(x - 3)^2+(y-(-5))^2=6^2$, which simplifies to $(x - 3)^2+(y + 5)^2=36$.

Answer:

D. $(x - 3)^2+(y + 5)^2=36$