Geometry

Question Analysis  

The main focus is to determine the equation of a horizontal parabola using its vertex, opening direction, and distance to the directrix to find the parameter .  

 

Key Concept Explanation  

Horizontal Parabola Form: For a parabola opening right with vertex , the standard form is , where p > 0. The directrix is a vertical line , and the distance from the vertex to the directrix is .  

 

Step-by-Step Solution  

1. Determine :  

The parabola opens right, so p > 0.  

Distance from vertex to directrix is (given). Thus, .  

2. Substitute into the standard form:  

Vertex: , .  

Equation:

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