Question

1. find the center and radius of the circle with equation ((x - 6)^2 + (y + 5)^2 = 9).

• center ((-6, 5)); radius 3
• center ((-6, 5)); radius 9
• center ((6, -5)); radius 3
• center ((6, -5)); radius 9

Explanation:

Step1: Recall circle standard form

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

Step2: Identify center coordinates

Compare $(x - 6)^2 + (y + 5)^2 = 9$ to the standard form:
Rewrite $y+5$ as $y-(-5)$, so $h=6$, $k=-5$. Center is $(6, -5)$.

Step3: Calculate the radius

The right-hand side is $9 = r^2$, so $r = \sqrt{9} = 3$.

Answer:

center (6, -5); radius 3