Find the centre and radius of the circle `ax^(2) + ay^(2) + 2gx + 2fy + c = 0` where `a ne 0`.

Explanation

To find the center and radius of the circle given by the equation \( ax^2 + ay^2 + 2gx + 2fy + c = 0 \) where \( a \neq 0 \), we can follow these steps:

### Step 1: Normalize the Equation
First, we need to make the coefficients of \( x^2 \) and \( y^2 \) equal to 1. We do this by dividing the entire equation by \( a \):

\[ \frac{ax^2}{a} + \frac{ay^2}{a} + \frac{2gx}{a} + \frac{2fy}{a} + \frac{c}{a} = 0 \]
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