Answer
Please see the graph.
Work Step by Step
$9x^2 > 4y^2 +144$
The related equation for this equation is as follows:
$9x^2=4y^2+144$
$9x^2-4y^2=4y^2+144-4y^2$
$9x^2-4y^2=144$
$(9x^2-4y^2)/144=144/144$
$x^2/16 -y^2/36=1$
We have four regions to test (for $x$): $[-∞, -4), (-4, 4), (4, ∞)$
We pick the points $(-5, 0)$, $(0,0)$, $(5,0)$
$(-5,0)$
$9x^2 > 4y^2 +144$
$9*(-5)^2 > 4*0^2 +144$
$9*25 >4*0+144$
$225 > 0+144$
$225 > 144$ (true, so we shade the area with this point)
$(0,0)$
$9x^2 > 4y^2 +144$
$9*0^2 > 4*0^2 +144$
$9*0 > 4*0 +144$
$0 > 0 +144$
$0 > 144$ (false)
$(5,0)$
$9x^2 > 4y^2 +144$
$9*(5)^2 > 4*0^2 +144$
$9*25 >4*0+144$
$225 > 0+144$
$225 > 144$ (true, so we shade the area with this point)
