Find the centre and radius of each of the following circle: `x^2+y^2-x+2y-3=0`

Explanation

To find the center and radius of the circle given by the equation \(x^2 + y^2 - x + 2y - 3 = 0\), we will rewrite the equation in the standard form of a circle's equation, which is \((x - h)^2 + (y - k)^2 = r^2\), where \((h, k)\) is the center and \(r\) is the radius.

### Step-by-Step Solution:

1. **Start with the given equation:**
\[ x^2 + y^2 - x + 2y - 3 = 0 \]
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