Math Is Fun Forum

ccmint

Member

Registered: 2009-10-11

Posts: 22

How to derive other equations from the general conic section equation?

I've just read the Conic Sections page and at the bottom it says that the general equation can be used to create equations for the circle, ellipse, parabola and hyperbola. How can I create those equations? BTW, I've search all of Google and couldn't find anything.

Thanks!

mikau

Member

Registered: 2005-08-22

Posts: 1,504

Re: How to derive other equations from the general conic section equation?

Here's the generlal conic equation: Ax2 + Bxy + Cy2 + Dx + Ey + F = 0

Basically you make different shapes by assigning values to the coefficients A,B,C,D, E and F. Usually what you do is make some of those values 0 so the terms dissapear! For instance,
let A=1,B=0,C=1,D=0, E=0 and F=-1, then the above equation becomes

(1)x^2 + 0xy + (1)y^2 + (0)x + (0)y +(-1) = 0
this simplifies to:
x^2 + y^2 = 1 which is the equation of a circle!

Or if you let A = 1, E=-1 and everything else zero, you get:
(1)x^2 + 0xy + (1)y^2 + (0)x+(-1)y + (0) = 0
this simplifies to y=x^2 which is a parabola!

So its all just a question of what coefficients should be zero!

Last edited by mikau (2009-12-07 18:45:58)

---

A logarithm is just a misspelled algorithm.

ccmint

Member

Registered: 2009-10-11

Posts: 22

Re: How to derive other equations from the general conic section equation?

Thanks for clearing that up for me!