Geometry

Question Analysis  

The main focus is to derive the equation of a parabola using the given vertex and focus, determining its orientation and key parameters.  

 

Key Concept Explanation  

Vertical Parabola Equation: When the vertex and focus share the same -coordinate, the parabola is vertical. The standard form is , where is the distance from the vertex to the focus.  

If p > 0, the parabola opens upward; if p < 0, it opens downward.  

 

Step-by-Step Solution  

1. Determine the orientation and :  

Vertex: , Focus: .  

Both have the same -coordinate (), so the parabola is vertical.  

Calculate : .  

2. Write the equation in standard form:  

Substitute , , and into

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