The given equation is:

\[
(x - 3)^2 = 4(y - 3)
\]

This is the standard form of a **parabola** equation. To interpret it:

- The equation \((x - h)^2 = 4p(y - k)\) represents a parabola that opens either upwards or downwards. 
- In this case, the vertex is at the point \((h, k)\).

### Step-by-step explanation:
1. The equation is already in the form \((x - h)^2 = 4p(y - k)\), where:
   - \(h = 3\)
   - \(k = 3\)
   - \(4p = 4\) implies that \(p = 1\)

2. This indicates:
   - The vertex of the parabola is at \((3, 3)\).
   - The parabola opens **upwards** since \(p > 0\).
   - The focal length (the distance from the vertex to the focus) is \(p = 1\).

### Parabola features:
- **Vertex**: \((3, 3)\)
- **Focus**: Since \(p = 1\) and the parabola opens upward, the focus is at \((3, 3 + 1) = (3, 4)\).
- **Directrix**: The directrix is a horizontal line below the vertex, given by \(y = 3 - 1 = 2\).
- **Axis of symmetry**: The axis of symmetry is the vertical line \(x = 3\).

Would you like more details on the graph or specific properties of this parabola?

Here are 5 related questions:
1. How do we find the equation of a parabola given the vertex and focus?
2. What is the general form of the parabola equation?
3. How do we calculate the latus rectum length in a parabola?
4. What are the properties of a parabola opening downward?
5. Can the same process be applied to find the directrix for horizontal parabolas?

**Tip:** For parabolas, always identify the vertex and direction of opening before proceeding to focus or directrix calculations.

Explore how to interpret and solve the parabola equation (x - 3)² = 4(y - 3). This problem covers key concepts in analytic geometry, including the vertex, focus, directrix, and axis of symmetry. Suitable for students in Grades 10-12.

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