`(x+3)^(2)+(y+1)^(2)=25`
The graph of the equation is a circle. What is the area, in square units, of the circle?

Options

A. `4pi`
B. `5pi`
C. `16pi`
D. `25pi`

Answer

To find the area of the circle represented by the equation \((x+3)^{2} + (y+1)^{2} = 25\), we can follow these steps:

### Step 1: Identify the standard form of the circle's equation
The standard form of a circle's equation is given by:
\[ (x - a)^{2} + (y - b)^{2} = r^{2} \]
where \((a, b)\) is the center of the circle and \(r\) is the radius.

### Step 2: Rewrite the given equation
The given equation is:
\[ (x + 3)^{2} + (y + 1)^{2} = 25 \]
We can rewrite it in the standard form:
\[ (x - (-3))^{2} + (y - (-1))^{2} = 5^{2} \]
From this, we can see that:
- The center of the circle is \((-3, -1)\)
- The radius \(r\) is \(5\) (since \(r^{2} = 25\))

### Step 3: Calculate the area of the circle
The area \(A\) of a circle is given by the formula:
\[ A = \pi r^{2} \]
Substituting the value of \(r\):
\[ A = \pi (5)^{2} = \pi \times 25 = 25\pi \]

### Conclusion
Thus, the area of the circle is:
\[ \boxed{25\pi} \]

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