Find the equation of a parabola whose focus and vertex are (0, 0) and (0, 2) respectively.

Explanation

To find the equation of a parabola whose focus is at (0, 0) and vertex is at (0, 2), we can follow these steps:

### Step 1: Identify the Focus and Vertex
The focus of the parabola is given as \( F(0, 0) \) and the vertex is given as \( V(0, 2) \).

### Step 2: Determine the Directrix
The vertex is the midpoint between the focus and the directrix. Since the focus is at \( (0, 0) \) and the vertex is at \( (0, 2) \), we can find the directrix. The distance from the vertex to the focus is \( 2 \) units (from \( y = 0 \) to \( y = 2 \)). Therefore, the directrix will be \( 2 \) units above the vertex, which gives us the equation of the directrix as:
\[
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