Question

1. which equation is correct for a circle centered at (5, - 13) with a radius of 11? (x - 5)^2+(y + 13)^2 = 11 (x + 5)^2+(y - 13)^2 = 121 (x - 5)^2+(y - 13)^2 = 121 (x - 5)^2+(y + 13)^2 = 121

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 the center and radius values

Given the center $(h,k)=(5, - 13)$ and radius $r = 11$. Substitute $h = 5$, $k=-13$, and $r = 11$ into the formula. We get $(x - 5)^2+(y-(-13))^2=11^2$, which simplifies to $(x - 5)^2+(y + 13)^2=121$.

Answer:

$(x - 5)^2+(y + 13)^2=121$