Quadrics

Planar Quadrics

General Eq: $A{x}^2+B{y}^2+Cxy+Dx+Hy+F=0$

Ellipse

$$\frac{x^2}{a}+\frac{y^2}{b}=1$$

Parabola

$$y=a{x}^2$$

Hyperbola

$$\frac{y^2}{b^2}-\frac{x^2}{a^2}=\pm 1$$

• -1 → Horizontal
• +1 → Vertical

Slant Asymptotes

$$y=\pm \frac{b}{a}$$

Quadric Surfaces

• General Eq: $A{x}^2+B{y}^{2}C{x}^2+Dxy+Hxz+Fyz+Px+Qy+Rz+J=0$