Question

Give the required elements of the hyperbola.

2y^2 - 3x^2 = 6

The value of a is:

√2
√3
2
3

Answer 1

Do I have to simplify first, or do I take the bigger number, which is 3?

Answer 2

to get this into standard form first divide both sides by 6

Answer 3

(1/3)y^2-(1/2)x^2=1

Answer 4

agreed. now compare this with the standard for of a hyperbola (centered at the origin):\[\frac{y^2}{b^2}-\frac{x^2}{a^2}=1\]

Answer 5

OOOOOh , So it's 3?

Answer 6

a is whichever number is bigger, right?

Answer 7

a^2 is the number under the x^2

Answer 8

Hahah thanks. It's so simple, but i'm completely clueless.

Answer 9

yeah. make sure you realize that a does not equal 2. a^2=2

Answer 10

@eseidl I'm pretty sure that \(a^2\) is always under the positive one in a hyperbola.
\[\frac{x^2}{a^2} - \frac{y^2}{b^{2}} = 1\]\[\frac{y^2}{a^2} - \frac{x^2}{b^2} = 1\]

Answer 11

GOD flutterING DAMN IT

Answer 12

@Calcmathlete let me check my text, you may be correct.

Answer 13

it's still 3 though?

Answer 14

If I am correct, then \(a^2 = 3\). You ned what \(a\) is.

Answer 15

square root of 3

Answer 16

@Calcmathlete I stand corrected. so a^2=3.

Answer 17

@idontgetconicsections THat works :) \(a = \sqrt{3}\).

Answer 18

So this conic has foci:\[(0,\pm c)\] where c^2=a^2+b^2=5
c=sqrt 5
It has vertices \[(0,\pm a)\]where a=sqrt 3
and asymptotes \[y=\pm (\frac{a}{b})x\]

Answer 19

also, It opens up/down