An SVM learns the parameters $a$, $b$, $c$ and $d$ of a separating hyperplane in the new space $\phi(\mathbf{x}) = \phi(\begin{pmatrix} x_1 \\ x_2 \end{pmatrix}) = \begin{pmatrix} x_1^2 \\ \sqrt{2}x_1x_2 \\ x_2^2 \end{pmatrix} = \begin{pmatrix}X\\Y\\Z\end{pmatrix}$, which has an equation of the form $aX+bY+cZ=d$. Take the particular case where $a=c=1$ and $b=0$, you obtain (with variables from the input space) the equation of a circle of radius $\sqrt{d}$ and center $(0, 0)$: $x_1^2 + x_2^2=d$. According to your figure, choose $d\approx0.7^2$, and this hyperplane should separate your data. Note that the SVM will probably not learn exactly these particular parameters ($a=c=1$, $b=0$, $d=0.7^2$). Based on the form of the kernel space, the SVM separating plane could be ellipses, hyperbolas or parabolas (see: https://en.wikipedia.org/wiki/Conic_section#General_Cartesian_form). However the SVM will learn the curve that separates the data with the larger margin. So probably that the result of your SVM should be an ellipse close to a perfect circle (with the center exactly in $(0, 0)$ because you don't have terms in just $x_1$ or $x_2$ in the equation of the ellipse, and according to this page: https://en.wikipedia.org/wiki/Ellipse#General_ellipse), and with radius between $0.6$ and $0.8$ or something like that (this is just by looking approximately on your figure).
