Answer:
y²=20x
Step-by-step explanation:
Note: I'm assuming you mean x=-5 for the directrix because what you're asking isn't possible
Since we are given a horizontal directrix, the parabola must also be horizontal.
Horizontal Parabola:
(y-k)² = 4p(x-h)
Vertex: (h, k)
Focus: (h+p, k)
Directrix: x = h - p
Since the focus of the parabola is (5,0), then k=0 and h+p=5. We also know that since the directrix is x=-5, then -5=h-p. If we set these equations equal to each other, we can solve for h and p:
h+p=5
h-p=-5
2p=10
p=5
Since p=5, then h=0. Therefore, we have for our equation of the parabola:
(y-k)² = 4p(x-0)
(y-0)² = 4(5)(x-0)
y²=20x
