Find the centre and radius of the circle `4x^(2) + 4y^(2) + 16y -4x = 19.`

Explanation

To find the center and radius of the circle given by the equation \(4x^2 + 4y^2 + 16y - 4x = 19\), we will follow these steps:

### Step 1: Rewrite the equation
First, we need to rewrite the equation in a standard form. The general equation of a circle is given by:
\[ x^2 + y^2 + 2gx + 2fy + c = 0 \]
To achieve this, we will divide the entire equation by 4 to make the coefficients of \(x^2\) and \(y^2\) equal to 1.
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