Question

Need help with literals C and D from question 1

Answer 1

C.

To find the x-intercepts we make y = 0 and solve for x:

`\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}`

x-intercepts: -2 and 2

To find the y-intercepts we make x = 0 and solve for y:

`\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}`

y-intercepts: -1 and 1

Performing the symmetry test, (replacing x for -x and y for -y)

`(-x)^2+4(-y)^2=4\rightarrow x^2+4y^2=4`

D.

Finding the intercepts,

`\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}`

x-intercepts: -1 and 1

`\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}`

y-intercepts: -2 and 2

Performing the symmetry test,

`4(-x)^2+(-y)^2=4\rightarrow4x^2+y^2=4`