Hi.

I'm just starting to learn about conic sections, and it says in my text that their general equation is .

Is that an error? Isn't it supposed to be not just ?

Thanks for your help.

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- July 7th 2009, 05:49 AMStroodleConic Sections
Hi.

I'm just starting to learn about conic sections, and it says in my text that their general equation is .

Is that an error? Isn't it supposed to be not just ?

Thanks for your help. - July 7th 2009, 05:54 AMyeongil
Yes, the x-squared is missing. Also, the xy term is missing. In my book the general form of a quadratic equation in 2 variables is

.

After a Google Search, I have found this equation also expressed as

,

which is closer to what you have.

01 - July 7th 2009, 06:03 AMStroodle
Awesome. Thanks for that.

Would the term be present for hyperbolas and ellipses also? As my text says that this general equation is for all conic sections... - July 7th 2009, 06:19 AMyeongil
Yes.

Actually, now that I think about it, if there is an xy term then the conic is**rotated**by some angle. You stated that you're starting to learn about conic sections, so the book probably omitted the xy term deliberately. This means that in parabolas & hyperbolas, without the xy term, the curves will only open upward/downward/left/right. And in ellipses, the major/minor axes will only be horizontal/vertical lines.

01 - July 7th 2009, 06:22 AMStroodle
Cool. Thanks for your help!