How to draw the graph of two curves look like a lemniscate which satisfy $d_1d_2=b$ where $b<a^2$ and $b>a^2$ respectively?

Question

Actually I was drawing the graph of a lemniscate with the help of a polar ordinate equation - $r^2=2a^2cos2\theta$ And for which I had to prove that the points lie on it would satisfy the condition $d_1d_2=a^2$ Where $d_1,d_2$ and $a$ for a point $P$ lie on the lamniscate are shown in the following figure it is the figure

Now I am looking for the graph of two curves which satisfy $d_1d_2=b$ where $b>a^2$ and $b<a^2$ respectively.Please help me.