Geometry

Question Analysis  

The main focus is to determine the focus of a horizontal parabola from its given equation. We need to rewrite the equation in standard form to identify the vertex and focal length.  

 

Key Concept Explanation  

Standard Form of a Horizontal Parabola: The equation represents a horizontal parabola with vertex . The focus is located at if a > 0 (opens right) or if a < 0 (opens left). Here, is the distance from the vertex to the focus.  

 

Step-by-Step Solution  

1. Rewrite the equation in standard form:  

Given , this is already in the form with , , and .  

2. Identify , , and :  

, so .  

Vertex: .  

3. Determine the focus:  

Since a > 0, the parabola opens to the right. The focus is unit to the right of the vertex:  

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