Find the equation of a parabola with focus F(0, -12) and directrix y = 12.

Question

anonymous · Answer

attachment

anonymous · Answer

@Timotheos

anonymous · Answer

Can u help plz

hartnn · Answer

Any point, (x, y) on the parabola satisfies the definition of parabola, so there are two distances to calculate:

Distance between the point on the parabola to the focus (a,b)
Distance between the point on the parabola to the directrix (y=c)

when we equate the SQUARE of these distances, we get 
$\large (x-a)^2 + (y-k)^2 = (y-c)^2$
for your question,
a = 0, b = -12 , c = 12
just plug in and simplify!

hartnn · Answer

** 
$\large (x-a)^2 + (y-b)^2 = (y-c)^2$

hartnn · Answer

x^2 + (y+12)^2  = (y-12)^2 
see whether you get 
x^2 = -48y 
or 
y = (-1/48)x^2 
(which is your choice A)