Question

What are the asymptotes of the hyperbola given by the equation y squared over 1minus x squared over 121 = 1?

Answer 1

\[\frac{ y ^{2} }{ 1 } - \frac{ x ^{2} }{ 121 } = 1\] This is of the form
\[\frac{ y ^{2} }{ a ^{2} } - \frac{ x ^{2} }{ b ^{2} } = 1\] This Hyperbola will have a graph like the following with ots vertex in the y axis.

Answer 2

Now \[a ^{2} = 1; \space so \space a = 1\]\[b ^{2} = 121; \space So \space b = 11\]

The asymptotes are given by the equation \[y = \pm \frac{ a }{ b } x\]

\[y = \pm \frac{ 1 }{ 11 }x\]