Given:
The focus of the parabola is at (-4,8).
The directrix is at x=-6.
To find:
The equation of the parabola.
Solution:
The directrix is at x=-6, which is a vertical line. So, the parabola is horizontal.
The equation of a horizontal parabola is
Where, (h,k) is vertex, (h+p,k) is focus and x=h-p.
The focus of the parabola is at (-4,8).
...(i)
The directrix is at x=-6.
...(ii)
Adding (i) and (ii), we get
Putting h=-5 in (i), we get
Putting h=-5, k=8 and p=1 in the standard form of the parabola.
Therefore, the required equation of the parabola is .