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 circle - equation formula

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

Step2: Identify the values of \(h\), \(k\), and \(r\)

Given that the center is \((- 3,-5)\), so \(h=-3\), \(k = - 5\), and the radius \(r = 6\).

Step3: Substitute the values into the formula

Substitute \(h=-3\), \(k=-5\), and \(r = 6\) into \((x - h)^2+(y - k)^2=r^2\). We get \((x-(-3))^2+(y - (-5))^2=6^2\), which simplifies to \((x + 3)^2+(y + 5)^2=36\).

Answer:

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