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)
