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
Equation of Circle
Equation of circle of radius R, center at (x0,y0)
(x - x0)2 + (y - y0)2 = R2
Equation of Circle of RadiusR Passing through Origin
r = 2R cos(θ — α)
where (θ, α) are polar coordinates of any point on the circle and (R, α) are polar coordinates of the center of the circle.
Conics [Ellipse, Parabola or Hyperbola]
If a point P moves so that its distance from a fixed point [called the focus] divided by its distance from a fixed line [called the directrix] is a constant e [called the eccentricity], then the curve described by P is called a conic [so-called because such curves can be obtained by intersecting a plane and a cone at different angles].
If the focus is chosen at origin O the equation of a conic in polar coordinates (r, θ) is, if OQ = p and LM = D,
The conic is
(i) an ellipse if ε < 1
(ii) a parabola if ε = 1
(iii) a hyperbola if ε > 1.
