Given that parabola has a focus of (-1,2) and directrix of x=5, Matching the steps with the equations we shall have:
1. Use (x,y)⇒choose a point from the parabola.
2. √[(x+1)²+(y-2)²]⇒Find the distance from the focus to the point on the parabola
3. √(x-5)²⇒Find the distance from the point on the parabola to the directrix
4. √[(x+1)²+(y-2)²]=√(x-5)²⇒Set the distance from focus to the point equal to the distance from directrix to the point
5. (x+2)²+(y-2)²=(x-5)² ⇒Square both sides and simplify
y²-4y+4=-12x+24
6. x=-y²/12+y/3+5/3⇒Write the equation of the parabola