### Conic Sections

**Parabola**

- Equation:
**(y^2=4ax)**, a real number - Focus:
**((a,0))**, the point *Directrix*:**(x=-a)**, the vertical with equation

**Ellipse**

- Equation:
**(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1)**, (a), (b) positive numbers. - Foci:
**((c,0),(-c,0))**, where, (c^2=a^2-b^2) - Directrices:
**(x=\pm\frac{a^2}{c})**, the vertical with equations - Eccentricity:
**(e=\frac{c}{a}), (0<e<1)**

**Hyperbola**

- Equation:
**(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1)**, (a), (b) positive numbers. - Foci:
**((c,0),(-c,0))**, where, (c^2=a^2+b^2) - Directrices: The vertical lines
**(x=\pm\frac{a^2}{c})** - Eccentricity:
**(e=\frac{c}{a}), (e>1)** - Asymptotes:
**(y=\pm\frac{b}{a}x)**