Question

Which equation represents an asymptote of this hyperbola?

((x - 1)^2)/6^2 - ((y - 2)^2)/8^2 = 1

Answer 1

@Michele_Laino

Answer 2

y = 2 + (4x)/3

Answer 3

y = (2 + 4x)/3

Answer 4

y = 2 + (3x)/4

Answer 5

y = (2 + 3x)/4

Answer 6

hint:
if we make this traslation:
x-1=X
y-2=Y
where X, Y are the new coordinates, then we can rewrite your hyperbola as below:
\[\frac{{{X^2}}}{{{6^2}}} - \frac{{{Y^2}}}{{{8^2}}} = 1\]

Answer 7

now, the asymptotes of that hyperbola are:
\[Y = \frac{8}{6}X = \frac{4}{3}X\]

Answer 8

Y = (4 x)/3

Answer 9

so it would be Y=2+4x/3

Answer 10

so we have:
\[y - 2 = \pm \frac{4}{3}\left( {x - 1} \right)\]
I have used +/- since we have 2 asymptotes, namely:
\[Y = \pm \frac{4}{3}X\]

Answer 11

so it would be y = (2 + 4x)/3

Answer 12

yes! It is one of our asymptotes

Answer 13

thx

Answer 14

thanks!