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Conics Equation help- Algebra

fireshot91

fireshot91

macrumors 601
Original poster
Jul 31, 2008
4,721
1
Northern VA
So, over Spring Break, my teacher assigned this packet on conics. One of the parts of the packet is to "simplify" (Or rather elongate) the equation into general form.

General form is ax^2+by^2+cx+dy+e=0, where A, B, C, D are all integers, and A is positive.

Well, I did that to an equation, but for the x^2 term, I have a negative number, so I have no idea what to do. Do I just make it ay^2+bx^2, etc, etc. (Like I did). Or did I do something wrong?

Forgot to add, this is happening on quite a few of them (1/3 of them about), so if this is wrong, then I'm basically screwed, and will get a bad grade on this project.
 

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Eraserhead said:
the first constant being negative should be fine.
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miles01110 said:
Why does A have to be positive? If A,B,C,D are integers, they can be negative as well. Looks like you did all the multiplication right to me, but I'm looking at it sideways :p
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Because my teacher said it had to be, and on the instructions it says it's not in General Form unless A is positive. But I got a friend's help; Multiply both sides by -1, since it's a 0 on the other side, it'd be the same.
 
You've done it completely right. Making the a positive is just to be picky and consistent.

If you really want to then just switch all the signs over so the a is positive....same as moving them all to the other side of the = sign, or multiplying by -1.

EDIT:
fireshot91 said:
Because my teacher said it had to be, and on the instructions it says it's not in General Form unless A is positive. But I got a friend's help; Multiply both sides by -1, since it's a 0 on the other side, it'd be the same.
Click to expand...

yeh. general form. making the a positive is just to be consistent. doesn't make any difference to the actual result of the equation.
 
fireshot91 said:
Multiply both sides by -1, since it's a 0 on the other side, it'd be the same.
Click to expand...

That is correct and will get the answer of the form you require. Just remember, what ever you do to the left hand side (LHS) you must do to the RHS.

If you are stuck on anything else, please feel free to ask.
 
ShaunPriest said:
If you are stuck on anything else, please feel free to ask.
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Yes, actually I am right about now.

I have 8 graphs (Hyperbolas, 4 Vertical, and 4 Horizontal). I have 8 equations in general form. How do I match the graph with each one, without actually using a calculator, or anything. Well, actually I have 16 equations, just that each of the 8 equation is in two forms, General and Standard I think.
 
fireshot91 said:
Yes, actually I am right about now.

I have 8 graphs (Hyperbolas, 4 Vertical, and 4 Horizontal). I have 8 equations in general form. How do I match the graph with each one, without actually using a calculator, or anything. Well, actually I have 16 equations, just that each of the 8 equation is in two forms, General and Standard I think.
Click to expand...

Are these equations similar to the initial one you posted?

Try using "Grapher". It should be in your Mac OS X Applications / Utility folder. I know you are not meant to use anything, but using a program will let you tinker with the equations to see how they are affected.

i.e. the original equation you posted: (y+2)^2 - 4(x - 1)^2 = 16, if you change the - 4 to a +4 it turns the graph upside down (it is reflected in the line y = 2).
 
fireshot91 said:
Yes, actually, the first one I posted (The picture) is one of the hyperbolas. I can't tell if it's vertical or horizontal.
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it's easier to go off the standard form and not the general. if the first variable you see is a y, then the hyperbola is vertical. if the first variable you see is x, then the hyperbola is horizontal. in the example above, because y comes first, it's vertical.

of course, some conditions have to be met. the leading variable term should be positive, and the constant on the other side (to be in standard form) should equal one.
 
Jeez, thank you. Grapher, which I didn't even know I had, really helped me fix my errors.


I've finally corrected my mistake, after a good two hours. Now time to continue with the assignment :mad:
 
miles01110 said:
Oh, you have no idea. I don't think I ever handed in an assignment in college that I didn't get called into the professor's office at least once to decipher it. One of my few shortcomings (har har).
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That's why I like email so much. All through gradeschool I was getting in trouble for having lousy handwriting. :apple: I would literally get yelled at on a consistent basis. :( That's where my hatred of the public school system comes from.
 
TechieJustin said:
That's why I like email so much. All through gradeschool I was getting in trouble for having lousy handwriting. :apple: I would literally get yelled at on a consistent basis. :( That's where my hatred of the public school system comes from.
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Didn't you ever think to do something about your handwriting? So, you know, you wouldn't get yelled at? Legible handwriting is important throughout life, not just gradeschool....
 
lukenn said:
Didn't you ever think to do something about your handwriting? So, you know, you wouldn't get yelled at? Legible handwriting is important throughout life, not just gradeschool....
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Yes. I made several attempts throughout the years - nothing took. Once I got to high school I started printing and nobody complained. Up to that point we were required to use cursive at all times.
 
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