Since the directrix is parallel to the x-axis, and is greater than the focus, the parabola opens to the left and the vertex, (h, k), will be half way between them.
Fx = 3
x = 5
h = (Fx + x) / 2
h = (3 + 5) / 2
h = 8 / 2
h = 4
k = Fy
k = 1
The directrix crosses the x-axis at (5, 0), so
y = 0
and
x = a(y - k)² + h
5 = a(0 - 1)² + 4
5 = a + 4
a = 5 - 4
a = 1
x = (y - 1)² + 4
x = (y² - 2y + 1) + 4
x = y² - 2y + 1 + 4
x = y² - 2y + 5
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