Math Is Fun Forum

KiWoonG

Guest

**_ Parametrics _**

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.

can somebody help me on this??

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: **_ Parametrics _**

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.

---

Why did the vector cross the road?
It wanted to be normal.

ajp3

Member

Registered: 2005-08-25

Posts: 9

Re: **_ Parametrics _**

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