Answer:
A. [tex]r^2=9\sin 2\theta.[/tex]
Step-by-step explanation:
The lemniscate of Bernoulli is a plane curve defined from two given points [tex]F_1[/tex]and [tex]F_2[/tex], known as foci, at distance 2a from each other as the locus of points P so that [tex]PF_1\cdot PF_2=a^2.[/tex]
The equation of the lemniscate of Bernoulli is
[tex]r^2=a^2\cos 2\theta[/tex]
or
[tex]r^2=a^2\sin 2\theta[/tex]
In your case, the lemniscate of Bernoulli is represented by the equation
[tex]r^2=9\sin 2\theta.[/tex]
See attached diagram for details.
