The centre and radius of the circle `(x+ 2)^(2) + (y+4)^(2) = 9` are

Options

A. (2, 4) and 3
B. `(-2, -4) and 3`
C. `(-2, -4)` and 9
D. `(2, -4)` and 3

Answer

To find the center and radius of the circle given by the equation \((x + 2)^2 + (y + 4)^2 = 9\), 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:
\[ (x + 2)^2 + (y + 4)^2 = 9 \]
We can rewrite this in a form that resembles the standard form:
\[ (x - (-2))^2 + (y - (-4))^2 = 3^2 \]

### Step 3: Compare the equations
Now, we can compare this rewritten equation with the standard form:
- From \((x - (-2))^2\), we see that \(a = -2\).
- From \((y - (-4))^2\), we see that \(b = -4\).
- The right side \(3^2\) indicates that \(r = 3\).

### Step 4: State the center and radius
Thus, we can conclude:
- The center of the circle is \((-2, -4)\).
- The radius of the circle is \(3\).

### Final Answer
- Center: \((-2, -4)\)
- Radius: \(3\)

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