Given:
The focus is at (0, -5/3)
The directrix is y = 5/3
A standard form of the equation for a parabola is
y = a(x- h)² + k
with the focus at (h , k + 1/(4a)),
and the directrix at y = k - 1/(4a)
Therefore
h = 0 (1)
k + 1/(4a) = -5/3 (2)
k - 1/(4a) = 5/3 (3)
Add (2) and (3).
2k = 0
k = 0
Therefore the vertex is at (0,0).
From (2), obtain
1/(4a) = -5/3
4a = -3/5
a = -3/20
The equation of the parabola is
y = -(3/20)x²
The graph is shown below.
Answer: [tex]y=- \frac{3}{20} x^{2}[/tex]
