Answer
$(-4,0),(4,0),(0,-2), \text{ and }(0,2)$.
Work Step by Step
The given equation is $x^2+4y^2=16$
To find the $x$ intercepts, set $y=0$, then solve for $x$.
$x^2+4(0)^2=16$
$x^2=16$
$x=\pm 4$
Hence the $x$ intercepts are $(-4,0),(4,0)$.
To find the $y$ intercepts, set $x=0$, then solve for $y$
$(0)^2+4y^2=16$
$4y^2=16$
$y^2=4$
$y=\pm 2$
Hence the $y$ intercepts are $(0,-2),(0,2)$
