# Curves

### Figure Eight Curve

- Cartesian equation:
- $x^{4} = a^{2}(x^{2}-y^{2})$

- Polar equation:
- $r^{2} = a^{2}\cos(2 \theta )\sec^{4}( \theta )$

### Description

This curve is also known as the*Lemniscate of Gerono*.

**Other Web site:**

Xah Lee

- Cartesian equation:
- $x^{4} = a^{2}(x^{2}-y^{2})$

- Polar equation:
- $r^{2} = a^{2}\cos(2 \theta )\sec^{4}( \theta )$

Xah Lee