Answer:
(x - 8)² = 20(y + 6)
Step-by-step explanation:
The focus of the parabola is (8,-1) and the equation of the directrix is y = - 11.
So, the parabola opens up and the axis of symmetry is x = 8 line.
Now, the axis of symmetry and the directrix meet at the point (8,-11).
So, the vertex of the parabola will be the midpoint of (8,-1) and (8,-11) i.e. (8,-6).
Now, half of the distance between the focus and the directrix is = a = units.
So, the equation of the parabola in vertex form will be
(x - 8)² = 4 × 5 × (y + 6)
⇒ (x - 8)² = 20(y + 6) (Answer)