Geometry

Question Analysis  

The main focus is to determine the focus of a parabola given its equation. We need to convert the equation to the standard form to identify key parameters (vertex, direction, and focal length).  

 

Key Concept Explanation  

Standard Form of a Vertical Parabola: For a parabola , the standard form is , where is the vertex. The focus of a vertical parabola is at when a > 0 (opens upward) or when a < 0 (opens downward). Here, represents the distance from the vertex to the focus.  

 

Step-by-Step Solution  

1. Rewrite the equation in standard form:  

The given equation is . Since there is no -term, it is already in vertex form with and .  

2. Identify , , and :  

Here, , , .  

3. Calculate the focal distance:  

The distance from the vertex to the focus is .  

4. Determine the focus coordinates:  

Since a > 0, the parabola opens upward. The focus is units above the vertex