202k views
4 votes
Use the Distance Formula to write an equation of the parabola with vertex (0,0) and focus (0, 5). An equation of the parabola is y=

User Wot
by
8.6k points

1 Answer

2 votes
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]
User Gooner
by
7.2k points

No related questions found