Question

Which of the following equations would graph a lemniscate?

Answer 1

A.
`r^2=9\sin 2\theta.`

Explanation:

The lemniscate of Bernoulli is a plane curve defined from two given points
`F_1`and
`F_2`, known as foci, at distance 2a from each other as the locus of points P so that
`PF_1\cdot PF_2=a^2.`

The equation of the lemniscate of Bernoulli is

`r^2=a^2\cos 2\theta`

or

`r^2=a^2\sin 2\theta`

In your case, the lemniscate of Bernoulli is represented by the equation

`r^2=9\sin 2\theta.`

See attached diagram for details.