Geometry

Question Analysis  

The main focus is to determine the equation of a parabola by analyzing the relationship between the given vertex and focus, identifying its orientation, and calculating key parameters.  

 

Key Concept Explanation  

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

If p > 0, the parabola opens right; if p < 0, it opens left.  

 

Step-by-Step Solution  

1. Determine the orientation and :  

Vertex: , Focus: .  

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

Calculate : .  

2. Write the equation in standard form:  

Substitute , , and into

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