Geometry

Question Analysis  

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

 

Key Concept Explanation  

Horizontal Parabola Directrix: For a parabola with vertex at the origin and focus , the parabola is horizontal. The directrix is a vertical line , equidistant from the vertex as the focus but in the opposite direction.  

 

Step-by-Step Solution  

1. Identify orientation and :  

Vertex: , Focus: .  

Both lie on the -axis, so the parabola is horizontal.  

The focus is at , so (positive, indicating the parabola opens to the right).  

2. Determine the directrix:  

For a horizontal parabola, the directrix is

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