A circle has a center at (−4, −5) and a radius of √6. What is the equation of the circle?

The correct answer is D. (x + 4)² + (y + 5)² = 6.

To find the equation of a circle with a given center and radius, we use the standard form of the equation:

[

(x – h)² + (y – k)² = r²

]

where ((h, k)) is the center of the circle and (r) is the radius.

In this case, the center is ((-4, -5)) and the radius is (sqrt{6}).

1. Substitute (h = -4) and (k = -5):

[

(x + 4)² + (y + 5)²

]

2. Next, square the radius (sqrt{6}):

[

(sqrt{6})² = 6

]

3. Combine the results:

[

(x + 4)² + (y + 5)² = 6

]

Thus, the equation of the circle is ((x + 4)² + (y + 5)² = 6), which matches option D.