Question

hyperbola

Answer 1

Find an equation in standard form for the hyperbola with vertices at (0, ±8) and asymptotes at y equals inverse of plus minus 1 divided by 2x.

Answer 2

okay so i get that a=+-8 but how do i find the rest of the equation?

Answer 3

like \[\frac{ y^2 }{ a^2 } -\frac{ x^2 }{ b^2 }\]

Answer 4

since a=+-8 wouldnt a^2 be 2sqrt2?

Answer 5

think you need
\[\frac{y^2}{64}-\frac{x^2}{b^2}=1\] right? you have

Answer 6

and you need \(b^2\) to finish it

Answer 7

asymptotes are
\[y=\pm\frac{1}{2}x\]??

Answer 8

i am asking, because it is hard for me to read what you wrote
are those the asymptotes?

Answer 9

let us assume that it is
then since the asympotes are
\[y=\frac{a}{b}x\] and you have \(a=8\) then
\[\frac{8}{b}=\frac{1}{2}\] making \(b=16\)
the equation will be
\[\frac{y^2}{8^2}-\frac{x^2}{16^2}=1\]

Answer 10

we can check it if you like

Answer 11

try to make this "asymptotes at y equals inverse of plus minus 1 divided by 2x." clearer if possible.