Geometry

Question Analysis  

The main focus is to determine the focus of a vertical parabola using the given vertex and directrix, leveraging the geometric relationship that the vertex is the midpoint between the focus and directrix.  

 

Key Concept Explanation  

For a vertical parabola with vertex , the directrix is a horizontal line , and the focus is , where is the distance from the vertex to the focus (and also to the directrix).  

 

Step-by-Step Solution  

1. Identify vertex and directrix coordinates:  

Vertex: → , .  

Directrix: .  

2. Calculate :  

The distance from the vertex's -coordinate to the directrix is . Thus, .  

3. Determine the focus:  

Since the parabola opens upward (directrix is below the vertex), the focus is units above the vertex:  

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