From the given graph,we find that the radius of the circle with center at the origin is r=4 units.
The equation of a circle with cter at the origin is
[tex]x^2+y^2=r^2[/tex]
Here, r is the radius of the circle.
Put r=4 in the above equation.
[tex]\begin{gathered} x^2+y^2=4^2 \\ x^2+y^2=16 \end{gathered}[/tex]
Multiply both sides of the above equation by 2.
[tex]\begin{gathered} 2x^2+2y^2=2\times16 \\ 2x^2+2y^2=32 \end{gathered}[/tex]
Therefore, the equation representing the circle is,
[tex]\begin{gathered} \\ 2x^2+2y^2=32 \end{gathered}[/tex]
