How to graph a lemniscate?

Question

Need to graph the lemniscate of. Bernoulli in geogebra 3d in the xy plane at z=5. I know how to graph the cartesian equation but not at z=5.

Answer 1

The variable, $a$ just controls the size of the figure. use this with correct multiplication signs as shown in the math.

Curve(a sqrt(2) cos(t) / (sin(t)² + 1), a sqrt(2) cos(t) sin(t) / (sin(t)² + 1), 5, t, 0, 2π)

$$\left(a\sqrt{2} \cdot \frac{\operatorname{cos} \left( t \right)}{\operatorname{sin} ^{2}\left( t \right) + 1},a \sqrt{2} \; \operatorname{cos} \left( t \right) \; \frac{\operatorname{sin} \left( t \right)}{\operatorname{sin} ^{2}\left( t \right) + 1}, 5 \right)$$