Question

How do you rotate axises for parabolas?

Answer 1

you mean when graphing or equations itself?

Answer 2

the equation modifications is what im thinking of

Answer 3

I got the concept of shift to polars; move; and unpolar

Answer 4

You end up with an dxy term iirc

Answer 5

right; thats if you simply want to make a concise equation out of it; but what if you want to simply take each point given and modify the x and y to match the rotation ... if that makes any sense

Answer 6

Or was that hyperbolics.. I can't recall. Been a while since I've done conic sections.

Answer 7

how about using conics Ax^2+Bxy+.....

Answer 8

http://www.stewartcalculus.com/data/CALCULUS%20Early%20Transcendentals/upfiles/RotationofAxes.pdf

Answer 9

take x^2 + 4 for instance;

take each point; convert to a polar coordinate; rotate it; then convert to rectangle. Will that rotate the parabola or just move it ?

Answer 10

id assume it rotates it with respect to the origin; but eveytime i try to script it i get a shift instead :)

Answer 11

u can use rotational transformation equations

Answer 12

\[y = x^2 + 4\]\[\implies r(sin\ \theta) = r^2(cos\ \theta)^2 + 4\]

I'm not sure how you are 'rotating' Are you just adding a shift to the theta?

Answer 13

given the standard polar coord setup: (r,theta), i should be able to add a shift to the original theta to swing the point around the origin while I retain the same r value

Answer 14

Yes, that works, but then how are you going back to rectangular?

Answer 15

http://www.wolframalpha.com/input/?i=polar+graph+rsin%28theta+%2B+pi%2F6%29+%3D+%28rcos%28theta+%2B+pi%2F6%29%29^2+%2B+4

Answer 16

tan(theta) provides the x and y values as far as i can think of

Answer 17

You have to use the sum of angles formula I think

Answer 18

that link you did; thats what i was trying to conjure up in me head :) thnx

Answer 19

\[\implies r\ sin(\theta + \phi) = r^2cos(\theta + \phi)^2 + 4\]\[\implies r[sin\theta cos\phi + cos\theta sin\phi] = r^2[cos\theta \cos\phi - sin\theta sin\phi]^2 + 4\]\[\implies rsin\theta cos\phi + rcos\theta sin\phi \]\[= r^2[(cos\theta \cos\phi)^2 -2(cos\theta sin\theta)(cos\phi sin\phi)+ (sin\theta sin\phi)^2]+ 4\]

Etc

Then you eventially change all your rcos(theta) to x and all your rsin(theta) to y, and all the sin and cos of phi you replace with the actual numbers. I'd guess you're gonna get at least an xy term in there as well as a y^2 term etc.

Answer 20

This might also be helpful..

http://en.wikipedia.org/wiki/Matrix_representation_of_conic_sections