Question

Determine whether it is a ellipse or hyperbola.

Answer 1

\[8x^2 - 2x = 8y - 3y\]

Answer 2

@pitamar You shall help me lol

Answer 3

is it 8y - 3y on the right? that is just 5y isn't it?

Answer 4

Oops typo it's 8y -3y^2 Wish it was that easy

Answer 5

It actually makes more sense =) it wouldn't be either if it was 5y..

Answer 6

ok, so let's see
we have

Answer 7

$$8x^2 - 2x = 8y - 3y^2$$Right?

Answer 8

Yea

Answer 9

Let's move everything to the left. what would that be?

Answer 10

8x^2 -2x - 8y -3y^2 = 0 ?

Answer 11

arm, you have a sign mistake there

Answer 12

Oh plus 3y^2

Answer 13

Yes, so
$$8x^2 - 2x + 3y^2 - 8y = 0 $$

Answer 14

Now, in fact I'd say that this is enough for us to tell what it really is..

Answer 15

Ellipse?

Answer 16

Yea so Ellipes I think

Answer 17

in fact I made a mistake I should ahve added factors to x and y.. which would make it uglier. let me fix it sec

Answer 18

Ellipse
$$(ax - h)^2 + (by-v)^2 = c^2$$
Hyperbola
$$(ax - h)^2 - (by-v)^2 = c^2$$

Answer 19

Now, we can see that in our case no matter what constants we add... we're still left with something like the first.. addition of two squares

Answer 20

So yes ellipse

Answer 21

So pretty much the difference in the to is add and subtract.

Answer 22

yep. addition of squares of subtraction of squares
Here is the graph btw:
http://www.wolframalpha.com/input/?i=8x%5E2+-+2x+%3D+8y+-+3y%5E2

Answer 23

Thanks man. You haven't failed me yet Lol

Answer 24

or*
sure no problem =)