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

1.
use (x, y).
find the distance from the point on the parabola to the directrix.

2.

set the distance from focus to the point equal to the distance from directrix to the point.

3.

find the distance from the focus to the point on the parabola.

4.

write the equation of the parabola.

5.

square both sides and simplify.

6.

choose a point on the parabola

The matched options to the given problem is below:

Step1: Choose a point on the parabola

Step2: Find the distance from the focus to the point on the parabola.

Step3: Use (x, y).

Find the distance from the point on the parabola to the directrix.

Step4: Set the distance from focus to the point equal to the distance from directrix to the point.

Step5: Square both sides and simplify.

Step6: Write the equation of the parabola.

Step by step Explanation:

Given that the focus (-1,2) and directrix x=5

To find the equation of the parabola:

By using focus directrix property of parabola

Let S be a point and d be line

focus (-1,2) and directrix x=5 respectively

If P is any point on the parabola then p is equidistants from S and d

Focus S=(-1,2), d:x-5=0

Step1: Let P(x,y) be any point on parabola

Step2: Therefore the

Step3: The perpendicular distance from p to d is

Step4: equating (1) and (2)

Step5: squaring on both sides

Step6: Equation of the parabola is

i think the correct option is the second option.