Consider we need to find the equation of the parabola.
Given:
Parabola with focus (2, 1) and directrix x=-8.
To find:
The equation of the parabola.
Solution:
We have directrix x=-8. so, it is a horizontal parabola.
The equation of a horizontal parabola is
...(i)
where, (h,k) is center, (h+p,k) is focus and x=h-p is directrix.
On comparing focus, we get
...(ii)
On comparing directrix, we get
...(iii)
Adding (ii) and (iii), we get
Divide both sides by 2.
Putting h=-3 in (ii), we get
Putting h=-3, k=1 and p=5 in (i), we get
Therefore, the equation of the parabola is .