Answer:
(y-8)² = -4 (x-4)
Explanation:
Directrix x=5 so we have a horizontal parabola
In general directrix for a horizontal parabola is x= h -p
Focus is (3, 8)
In general focus for a horizontal parabola is (p+h, k)
From this we can conclude that:
k=8
h -p =5
h+p = 3
We have two equation with two unknown. We can solve and find h and p.
h -p =5 → h = p+5
h+p = 3 → p+5+p = 3 → 2p = 3-5 → p = -2/2 → p = -1
h = p+5 → h = -1+5 → h = 4
Standard equation of a horizontal parabola is
(y - k)² = 4p (x - h), substitute k= 8, p= -1, and h=4
(y - 8)² = 4(-1) (x - 4)
(y - 8)² = -4 (x - 4)