Answer
Please see the graph.
Work Step by Step
$x^2/4 – y^2 < 1$
We pick the points $(-3,0)$, $(1,0)$, and $(3,0)$ to determine what side of the line to shade.
$(-3,0)$
$x^2/4 – y^2 < 1$
$(-3)^2/4 –0^2 < 1$
$9/4 -0 <1$
$9/4 < 1$ (false)
$(1,0)$
$x^2/4 – y^2 < 1$
$1^2/4 – 0^2 < 1$
$1/4 – 0 <1$
$1/4 < 1$ (true, so we shade the side of the line with this point)
$(3,0)$
$x^2/4 – y^2 < 1$
$(3)^2/4 –0^2 < 1$
$9/4 -0 <1$
$9/4 < 1$ (false)
