Question

Find the standard form of the equation of the parabola with a focus at (0, 6) and a directrix at y = -6.

Answer 1

here the vertex is origin
hence the required parabola
is
x^2= 4*6*y
x^2=24y

Answer 2

well, another way of doing it is:
\[\sqrt{x ^{2}+(y-6)^{2}} =0+y+6/1\],
so, x^2=24y
I have equated the perpendicular distance from a point P(x,y) on the directrix y+6=0, and the distance of point P from the focus.....from the basic definition of parabola, these two distances should always be equal...

Answer 3

thank you i recognize the second way more. :)

Answer 4

U are welcome!