Geometry

Question Analysis  

The main focus is to determine the focus of a vertical parabola using the vertex and directrix. Key relationship: the vertex is the midpoint between the focus and directrix.  

 

Key Concept Explanation  

For a vertical parabola, the vertex is equidistant from the focus and the directrix , where is the distance from the vertex to the focus/directrix.  

 

Step-by-Step Solution  

1. Identify vertex coordinates: .  

2. Analyze directrix equation: (horizontal line, so vertical parabola).  

3. Calculate :  

Distance from vertex to directrix: . Thus, .  

4. Find focus coordinates:  

For a vertical parabola opening upward (since directrix is below the vertex), focus is units above the vertex:  

(h, k + p) = (-1, 4 + 2) = (-1, 6).

 

Common Mistakes  

Misplacing the focus direction: forgetting that if the directrix is below the vertex, the focus is above (and vice versa).  

Confusing horizontal/vertical parabola formulas: mixing and

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