determine the equations of parabola with focus and directrix given ... focus(0,8) directrix y=0?

Question

i dont understand it please explain!!

Answer 1

F(0,8) directrix y=0
Take a point (x,y) of this parabola
(x-0)^2 +(y-8)^2 =y^2 ====> x^2 +y^2 -16y+64 =y^2

y= (1/16)*x^2 +4

Answer 2

for every parabola the distance from any point P(x,y) to the focus F and to the directrix y is the same, that is
PD = PF
using the formula for the distance, we get:
PD = sqrt[(x-x)^2 + (y-0)^2]
PF = sqrt [(x-0)^2 + (y-8)^2]
You equate the distances and simplify the equation. The equation is the equation of a parabola with the given condition.

If you have any additional questions, post them

Good Luck
Dorota

Answer 3

you should really do your own home work........