Step 1: Identify the vertex and focus of the parabola.
• Vertex: Given as (0,0).
• Focus: Given as (0,5).
Step 2: Find the value of ‘p’, which is the distance from the vertex to the focus. You can use the distance formula for this:
[p = \sqrt{(0 - 0)^2 + (5 - 0)^2} = \sqrt{0 + 25} = \sqrt{25} = 5]
Step 3: Use the information to write the equation of the parabola in the form:
[4p(y - k) = (x - h)^2]
• Vertex (h, k) = (0, 0)
• Value of ‘p’ is 5
Step 4: Plug the values into the equation:
[4(5)(y - 0) = (x - 0)^2]
Step 5: Simplify the equation:
[20y = x^2]
So, the equation of the parabola is:
[y = \frac{1}{20}x^2]