Answer
$(a)$ Symmetry with respect to $y$-axis and $x$-axis.
$(b)$ $x$-intercept $A(-4,0)$ and $B(4,0)$
$y$-intercept doesn't exist
Work Step by Step
$(a)$ As we can see from the image of the graph above, it is symmetrical with respect to the $y$-axis and $x$-axis.
Algebraically, if we replace either $x$ by $-x$ or $y$ by $-y$ equation will be still equivalent to the original one.
$(b)$
$x$-intercept happens when $y=0$
$9x^2-16\times0^2=144$
$9x^2=144$
$x^2=\frac{144}{9}$
$x=±\sqrt{\frac{144}{9}}$
$x_1=-4$
$x_2=4$
$A(-4,0)$ and $B(4,0)$
$y$-intercept happens when $x=0$
$9\times 0^2-16y^2=144$
$-16y^2=144$
$y^2=-\frac{144}{16}$
A number squared cannot have a negative value, so such $y$ doesn't exist. There is no $y$-intercept.
