Analytic Geometry- Lobachevski-Non-Euclidean Geometry
- Spherical Triangle
Definition of a Derivative- Matrices
- Binomial Coefficients
- Series
- Complex Numbers
- Indefinite Integrals
- Integrals
- Probability Theory
- Hyperbolic Functions
- Differential Equations
- Beta Function
Ellipse, Parabola, Hyperbola
Ellipse with center C(x0, y0) and major axis parallel to x axis
Length of major axis A'A — 2a
Length of minor axis B'B = 2b Distance from center C to focus F or F' is
Eccentricity = ε = c/a = 
Equation in rectangular coordinates:
Equation in polar coordinates if C is at O:
Equation in polar coordinates if C is on x axis and F' is at 0:
If P is any point on the ellipse, PF + PF' = 2a
If the major axis is parallel to the y axis, interchange x and y in the above or replace θ by ½π - θ [or 90° - θ].
Parabola with axis parallel to x axis
If vertex is at A(x0,y0) and the distance from A to focus F is a > 0, the equation of the parabola is if parabola opens to right
If parabola opens to left
If focus is at the origin the equation in polar coordinates is
In case the axis is parallel to the y axis, interchange x and y or replace θ by ½π — θ [or 90° — θ].
Hyperbola with center C(x0, y0) and major axis parallel to x axis
Length of major axis A'A = 2a
Length of minor axis B'B = 2b
Distance from center C to focus F or F' = c = 
Eccentricity ε = c/a = /a
Equation in rectangular coordinates:
Slopes of asymptotes G'H and GH' = ±b/a
Equation in polar coordinates if C is at O:
Equation in polar coordinates if C is on X axis and F' is at O:
If P is any point on the hyperbola, PF - PF' = ±2a [depending on branch]
If the major axis is parallel to the y axis, interchange x and y in the above or replace θ by ½π - θ [or 90° - θ].
