Question

Match the steps to find the equation of the parabola with focus (-1,2) and directrix x=5

Answer 1

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