Question

10. Write the equation of a hyperbola with vertices (0, -2) and (0, 2) and co-vertices (-4, 0) and (4, 0). MEDAL WILL BE GIVEN ! (づ￣ ³￣)づ

Answer 1

i think you have it, give me one second to check

Answer 2

oh hold on maybe not

Answer 3

oh ok lets draw a picture

Answer 4

wow damned ugly picture, but that is from the info given
verices at \((0,2)\) and \((0,-2)\)
from the orientation, can you tell what comes first, the
(x^2\) or the \(y^2\) ?

Answer 5

yes

Answer 6

and what number goes underneath the \(y^2\) ?

Answer 7

it is 4 because it crosses at 2 and \(2^2=4\)

Answer 8

so you know it is
\[\frac{y^2}{4}-\frac{x^2}{b^2}=1\] now how about \(b\) ?

Answer 9

hold on, don't forget you know the co vertices are \((-4,0)\) and \((0,4)\)
use that to find the number that goes under the \(x^2\) term

Answer 10

yeah, well i got froze out for a while
anyway, can you see what goes under the \(x^2\) term? don't forget it is a square

Answer 11

yes

Answer 12

\[\frac{y^2}{4}-\frac{x^2}{16}=1\]