C.
To find the x-intercepts we make y = 0 and solve for x:
[tex]\begin{gathered} x^2+4y^2=4 \\ \rightarrow x^2=4\rightarrow x=\pm\sqrt[]{4} \\ \Rightarrow x_1=-2,x_2=2^{}_{} \end{gathered}[/tex]
x-intercepts: -2 and 2
To find the y-intercepts we make x = 0 and solve for y:
[tex]\begin{gathered} x^2+4y^2=4 \\ \rightarrow4y^2=4\rightarrow y^2=1\rightarrow y=\pm\text{ }\sqrt[]{1} \\ \Rightarrow y_1=-1,y_2=1 \end{gathered}[/tex]
y-intercepts: -1 and 1
Performing the symmetry test, (replacing x for -x and y for -y)
[tex](-x)^2+4(-y)^2=4\rightarrow x^2+4y^2=4[/tex]
D.
Finding the intercepts,
[tex]\begin{gathered} 4x^2+y^2=4 \\ \rightarrow4x^2=4\rightarrow x^2=1\rightarrow x=\pm\text{ }\sqrt[]{1} \\ \Rightarrow x_1=-1,x_2=1 \end{gathered}[/tex]
x-intercepts: -1 and 1
[tex]\begin{gathered} 4x^2+y^2=4 \\ \rightarrow y^2=4\rightarrow y=\pm\text{ }\sqrt[]{4} \\ \Rightarrow y_1=-2,y_2=2 \end{gathered}[/tex]
y-intercepts: -2 and 2
Performing the symmetry test,
[tex]4(-x)^2+(-y)^2=4\rightarrow4x^2+y^2=4[/tex]
