Find the centre and radius of the circle `(x+1)^2+(y−1)^2=4`

Answer

To find the center and radius of the circle given by the equation \((x + 1)^2 + (y - 1)^2 = 4\), 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:
\[ (x - h)^2 + (y - k)^2 = r^2 \]
where \((h, k)\) is the center of the circle and \(r\) is the radius.

### Step 2: Rewrite the given equation
The given equation is:
\[ (x + 1)^2 + (y - 1)^2 = 4 \]
We can rewrite this in the standard form:
\[ (x - (-1))^2 + (y - 1)^2 = 2^2 \]
Here, we see that \(4\) can be expressed as \(2^2\).

### Step 3: Compare with the standard form
From the rewritten equation, we can identify:
- \(h = -1\)
- \(k = 1\)
- \(r^2 = 4\) which means \(r = 2\)

### Step 4: State the center and radius
Thus, the center of the circle is:
\[ (-1, 1) \]
And the radius of the circle is:
\[ 2 \]

### Final Answer
- Center: \((-1, 1)\)
- Radius: \(2\)

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