Answer:
To find the focus and directrix of the parabola given by the equation (x - 3)^2 = 4(y - 3) \), we can compare it with the standard form of the parabola equation \( (x - h)^2 = 4p(y - k) \), where \((h, k)\) is the vertex and \(p\) is the distance between the vertex and the focus (or the vertex and the directrix).
Comparing the given equation with the standard form, we can see that \(h = 3\) and \(k = 3\). Also, \(4p = 4\), so \(p = 1\).
Therefore, the vertex is at \((3, 3)\), the focus is \(1\) unit above the vertex at \((3, 3 + 1) = (3, 4)\), and the directrix is \(1\) unit below the vertex, which is the line \(y = 3 - 1 = 2\).
So, the focus is at \( (3, 4) \) and the directrix is \( y = 2 \).
