Question

I have a couple of practice problems that i need help in ! medals!

Answer 1

Graph the hyperbola with equation

Answer 2

my options

Answer 3

@ganeshie8

Answer 4

I remember once in my lifetime, I studied these things and now I have become rusty over these topics, so I fully give this responsibility to @ganeshie8 .

Answer 5

:)

Answer 6

Or other useful and helping members may help here.. :)

Answer 7

@ganeshie8 don't tell me you are also like me... :P

Answer 8

i think eliminating few options based on `center` would be a good place to start

Answer 9

i forgot the actual method to work these haha!
from the equation it seems the center is definitely NOT (0, 0) - based on just this info which two options can u eliminate @mondona ?

Answer 10

B and C (:

Answer 11

Perfect !

Answer 12

any ideas on how to decide whether its A or D ?

Answer 13

i have no idea :(((((((

Answer 14

let me look in my book again

Answer 15

Notice that A is standing straight UP-DOWN
and D is sleeping LEFT-RIGHT

Answer 16

yes i see that

Answer 17

\[\frac{ (x-h)^2 }{ a^2 }-\frac{ (y-k)^2 }{ b^2 }=1\]
This is a horizontal (x term is positive) hyperbola

for vertical the equation looks like this,

\[\frac{ (y-k)^2 }{ a^2 }-\frac{ (x-h)^2 }{ b^2 }=1\]

where your center is (h,k)

Answer 18

so my answer would be D

Answer 19

Yeah Batman is saying right.. He can't do unfair with the people of Gautham City(Openstudiers.. :)

Answer 20

D is \(\large \color{Red}{\checkmark }\)

Answer 21

Yes, D is correct.

Just to add a bit more information, a = transverse semi - axis (positive denominator), distance from centre to vertex.
b = conjugate semi - axis (the negative denominator).
c = distance from centre to focus. (Always largest)

So if you had this,

this is essentially what's going on in an horizontal hyperbola, these things are quite neat, also remember for the hyperbola only: c^2=a^2+b^2. I could give you more examples but Idk if you're interested or not haha, I personally find them quite neat.