Parabola as locus (1 Viewer)

[Thatstudentm9]

hey guys did i do this question correctly I've provided full working out of what i did

 

[pikachu975]

General form of a parabola at the origin is x^2 = 4ay but it's upside down so x^2 = -4ay
a = 4
x^2 = -16y

 

[Sp3ctre]

The parabola is concave down since the directrix is above the focus (from the graph), therefore the generation equation for this parabola is (x-h)^2 = -4a(y-k).

Since you've worked out the centre (h,k) which is at (0,0), and that a=4, substitute those values into the generation equation and you will get (x-0)^2 = -4*4(y-0).

So the final equation will be x^2 = -16y