use the focus directrix form of the eqn of a parabola:

x² = 4py (or y² = 4px for the horizontal case); note that p = the distance from the vertex to the focus = the distance from the vertex to the directrix

now, mathsyperson has already done most of the work!

take x² = 16y = 4(4y), so we see p = 4.

this means our parabola (with vertex (0,0) ) has focus (0, 4) and directrix y = -4

mathsyperson

2005-08-13 00:14:52

I'm not sure what you mean by focus and directix, but it's easy enough to convert it into a normal cartesian equation. x=8t t=x/8 y=4t² y=4(x/8)² y=4(x²/64) y=x²/16

And from that, you should be able to get any information you want.

KiWoonG

2005-08-12 22:52:49

Hi,, i needed help for parametrics,, here's a sample question,,,

A parabola has parametric equations x=8t and y=4t^2 Find the coordinates of its focus and equation of its directix.