Question

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Answer 1

The distance between any point (x,y) on the parabola and the focus equals the distance of that point from the directrix.

Use the distance formula to find the distance between (x,y) and the focus (-5,-5).

The distance between (x,y) and directrix here is: |(y-7)|.
Equate the two distances and simplify to find the equation of the parabola.

Answer 2

so a? @ranga

Answer 3

Distance between (x,y) and (-5,-5) = sqrt{ (x+5)^2 + (y+5)^2 }
Distance between (x,y) and directrix = |y-7|
The distances should be the same.
Square both sides and equate:
(x+5)^2 + (y+5)^2 = (y-7)^2
(x+5)^2 = (y-7)^2 - (y+5)^2 = (y-7+y+5)(y-7-y-5) = (2y-2)(-12) = -24(y-1)
divide both sides by -24 and then add 1:
-1/24(x+5)^2 + 1 = y or
y = -1/24(x+5)^2 + 1