Question

Which equations represent hyperbolas?
Please help, will fan and medal!

Answer 1

2x^2 + 16x + 2y^2 + 14y − 9 = 0
2x^2 + 4x − 5y^2 − 10y + 57 = 0
-x^2 + 5x − 7y^2 + 2y − 81 = 0
x − 2y^2 + 4y + 15 = 0
-x^2 + 12x + 3y^2 + 7y + 11 = 0

Answer 2

@jim_thompson5910

Answer 3

Okay... this is a bit complicated to fully explain. Hmm, firstly, do you know how to complete the square?

Answer 4

Any equation which HAS both an x^2 and a y^2 term, but both are NOT the same sign.

Answer 5

I know nothing about this

Answer 6

Everything you need is in my last post.

Answer 7

Feeling really stupid, but I still dont get it

Answer 8

The only stupid thing is to think that you're stupid. :P

Answer 9

Take a look at this:
https://www.mathsisfun.com/algebra/completing-square.html

Answer 10

It's very important thing to learn tbh!

Answer 11

Okay, so let me give you an example

Answer 12

But how does that show me which ones represent hyperbolas? I'm completely new to this course so I'm extremely confused

Answer 13

That's the general shape of a hyperbola

Answer 14

Any equation which HAS both an x^2 and a y^2 term, but both are NOT the same sign.

Eg. 2x^2 + y - 5y^2 - 6x = 0

IS a hyperbola because it has BOTH an x^2 and a y^2 term, but one is positive and one is negative, so they aren't the same sign.

Answer 15

Give me a sec :P

Answer 16

@Bobo-i-bo you don't need to complete the square to tell if they're hyperbolas or not.

Answer 17

Ohhh, okay.

Answer 18

No indeed you don't, but if you want to fully understand hyperbolas and stuff, it's better... it's better to give a man a net rather than one fish afterall. :P

Answer 19

So the hyperbolas would be the second and last equations

Answer 20

Play around with this: https://www.desmos.com/calculator/jvt3ahfmix

Answer 21

Yes @Bobo-i-bo , in general you need to know how to do other things to deal with them, but not to identify whether it's a hyperbola - in that case it's better to just know how to identify them.

Answer 22

@love_to_love_you correct. The second and last are the only hyperbolas.

Answer 23

Currently it is a circle. Now try setting either a or b to be negative. Play around with the values :)

Answer 24

@agent0smith I guess :P But personally understanding is more important to me.

Answer 25

@Bobo-i-bo understanding what? Understanding how to identify them is what's important here. That's a whole section of conics - knowing how to identify just by looking at the equation.

@love_to_love_you if you really have no idea about this topic, I'd find it on khanacademy... you aren't going to learn the entire topic here on openstudy. There's a lot to learn about hyperbolas, as well as ellipses and parabolas.

Answer 26

Completing the square is not the way to identify a conic. That's far too tedious to identify a conic. Ideally, a student should understand that long before they get to the point of identifying a conic section from an equation (which is meant to be after they've learned about all the conic sections).

"personally understanding is more important to me"... makes it seem like you didn't realize there was an alternative method to identify conics.

Answer 27

It's alright, I think we're going to get a tutor for this, in the meantime I just need help on a few questions

Answer 28

I'd recommend that, this is a pretty tough area of algebra 2, and it's easier to learn about these in person when someone can show it to you easily.