Question

use the equation of a parabola in standard form having a vertex at (0, 0), x^2= 8y.Solve the equation for "p" and then describe the focus (0, p), the directrix, and the 2 focal chord endpoints.

Answer 1

We have the following equation:

`x^2=8y`

the general formula for a parabola is given by:

`(x-h)^2=4p(y-k)`

Where (h,k) =(0,0) represent the vertex, so then our equation is:

`x^2=4py`

By direct comparison we have this:

4p= 8

p = 2

Then the focus is given by:

(0,p) = (0,2)

the directrix is given by:

y= 0-p = 0-2= -2

y=-2

And finally the 2 focal chord endpoints are:

`(|2p|,p)=(4,2),(-|2p|,p)=(-4,2)`