Question

the equation below describes a circle. what are the coordinates of the center of the circle? (x - 6)^2+(y + 5)^2 = 15^2 a. (6, -5) b. (-6, 5) c. (6, 5) d. (-6, -5)

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 center - coordinates

For the given equation $(x - 6)^2+(y+5)^2 = 15^2$, we can rewrite $(y + 5)^2$ as $(y-(-5))^2$. Comparing with the standard form $(x - a)^2+(y - b)^2=r^2$, we have $a = 6$ and $b=-5$.

Answer:

A. $(6,-5)$