Geometry

Question Analysis

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

 

Key Concept Explanation

For a vertical parabola opening down with vertex , the focus is p units below the vertex, and the directrix is p units above the vertex. The standard form is  with p < 0.

 

Step-by-Step Solution

Determine p:

The parabola opens down, so p < 0.

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

Write the equation: Substitute , ,  into 

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