Answer:
The answer to your question is y = 1/12 (x - 5)²
Step-by-step explanation:
Data
directrix y = -3
focus (5, 3)
Process
1.- Graph the directrix and focus to determine if the parabola is vertical or horizontal.
From the graph we know that it is a vertical parabola with equation
(x - h)² = 4p(y - k)
2.- From the graph we know that p = 3 because the distance from the focus to the directrix is 6 and p = 6/2.
3.- The vertex (5, 0)
4.- Substitution
(x - 5)² = 4(3)(y - 0)
5.- Simplification
(x - 5)² = 12y
6.- Result
y = 1/12 (x - 5)²
