Which equation represents a circle with a center at (-3, -5) and a radius of 6 units?
(x - 3)² + (y - 5)² = 6
(x - 3)² + (y - 5)² = 36
(x + 3)² + (y + 5)² = 6
(x + 3)² + (y + 5)² = 36

Solution:

We have standard form of the equation of circle whose centre at (h, k) and radius r as (x - h)² + (y - k)² = r²

For example, if the equation of the circle is (x + 6)² + (y - 5)² = 64, then centre is (h, k) = (-6, 5) and radius r = 8

Given: Center (h, k) = (-3, -5) and radius r = 6

Substituting in the standard form of the equation of circle, we have

⇒ [x - (-3)]² + [y - (-5)]² = 6²

⇒ (x + 3)² + (y + 5)² = 36

Therefore, the equation of circle is is (x + 3)² + (y + 5)² = 36.

Which equation represents a circle with a center at (-3, -5) and a radius of 6 units?

Summary: 

The equation that represents a circle with a center at (-3, -5) and a radius of 6 units is (x + 3)² + (y + 5)² = 36.