# How do you graph #r^2=cos(2theta)#?

##### 1 Answer

Called Lemniscate, the graph looks like

#### Explanation:

In the 1st and 4th quadrants,

I used infinity symbol

loop, looking like a fallen 8. For getting 8-erect, the equation is

Use a table

is the other loop.

Strictly,

Graphs of both

graph{((x^2+y^2)^2-x^2+y^2)((x^2+y^2)^2+x^2-y^2)=0[-2 2 -1 1]}.

Interestingly, an easy rotation of this graph through

produces a grand 8-petal flower.

graph{((x^2+y^2)^2-x^2+y^2)((x^2+y^2)^2+x^2-y^2)((x^2+y^2)^2-2xy)((x^2+y^2)^2+2xy)=0[-2 2 -1 1]}.