Answer
The x-intercepts are (-4,0) and (4,0)
The y-intercepts are (0,-2) and (0,2)
The equation has symmetry with respect to the x-axis, y-axis and origin.
Work Step by Step
To find the x-intercept, we set y to 0 and solve for x:
$x^2+4(0)^2=16$
$x^2=16$
$\sqrt(x^2)=\sqrt(16)$
$x=\pm4$
To find the y-intercept, we set x to y and solve for y:
$0^2+4y^2=16$
$4y^2=16$
$y^2=4$
$\sqrt(y^2)=\sqrt(4)$
$y=\pm2$
To test for symmetry with respect to the x-axis, we substitute y for -y and check if it equals the original equation:
$x^2+4(-y)^2=16$
$x^2+4y^2=16 \checkmark$
To test for symmetry with respect to the y-axis, we substitute x for -x and check if it equals the original equation:
$(-x)^2+4y^2=16$
$x^2+4y^2=16\checkmark$
To test for symmetry with respect to the origin, we substitute x for -x, substitute y for -y and check if it equals the original equation:
$(-x)^2+4(-y)^2=16$
$x^2+4y^2=16\checkmark$