Question

hello....can someone tell me what happens if the directrix of a parabola is inclined???...

Answer 1

isnt the directrix perpendicular to the parabola?

Answer 2

if the directrix becomes inclined, then the parabola is inclined. and we get an xy term in the process

Answer 3

Hey....thanks for replying.....The definition of a parabola is like its a curve who's points are equidistant from a given point and a given line....

Answer 4

it can be like that, in fact theres a general conic form that i cant remember that would allow for inclines

Answer 5

mathically: given a focus(u,v) and a directrix (y=mx+b)

then all points that are equidistance can be determined, but its a real pain to work out on here lol

Answer 6

k man....ill give it a try....and come on.....math isn't a pain...:)

Answer 7

math aint, but typing is :)

Answer 8

one method is to simply take a parabola: y = a(x-h)^2+k

and run it thru a rotation matrix

Answer 9

x^ = x cos(t) - y sin(t)
y^ = x sin(t) + y cos(t)

etc ...

Answer 10

ok...but my focus is still on the axis....it will get shifted wouldn't it?

Answer 11

The other term you can researc this under is an oblique directrix. That gets some book results.

Answer 12

hey e.mccormick...thanks...ill check dat out..:)

Answer 13

or general conic form

http://staff.argyll.epsb.ca/jreed/math30p/conics/general.htm

Answer 14

when the xy term zeros out, the conic is parallel to the x or y axis

Answer 15

ok...:)