Question

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

Explanation:

Step1: Recall the standard form of a circle's equation

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

Step2: Substitute the given center and radius

Given \(h=-3\), \(k = - 5\), \(r = 6\).
Substitute into the formula: \((x-(-3))^2+(y-(-5))^2=6^2\).
Simplify to get \((x + 3)^2+(y + 5)^2=36\).

Answer:

\((x + 3)^2+(y + 5)^2=36\) (the fourth option)