Final answer:
The circle with the equation (x-6)^2+(y+5)^2=5 is centered at (6, -5) with a radius approximately 2.236, and it lies entirely in the fourth quadrant.
Step-by-step explanation:
The given equation represents a circle with a center at (6, -5) and a radius of √5, which is approximately 2.236. Since the center of the circle has a positive x-coordinate and a negative y-coordinate, it lies in the fourth quadrant. However, because the radius stretches out from the center, part of the circle may extend into the third quadrant, depending on the location of the center relative to the radius length. To determine which quadrants the circle passes through, we can add and subtract the radius from the center's coordinates. Adding the radius to the x-coordinate (6 + 2.236) and subtracting it from the y-coordinate (-5 - 2.236) will give the farthest extents of the circle on the coordinate plane. The circle, in this case, doesn't stretch into other quadrants, it remains entirely within the fourth quadrant since the altered coordinates (6 + 2.236, -5 - 2.236) are still in the fourth quadrant, demonstrating that the circle does not cross into the third quadrant.