Key Polar Graphs Lemniscates

What type of graph is this?

What type of graph is this?

Lemniscates

r² = a²cos(2θ)/r² = a²sin(2θ): a ?

petal length (must square root it)

r² = a²cos(2θ): petals placement ?

petals lies over polar axis

r² = a²sin(2θ): petals placement ?

petals are at 45° off of axis