Equation of Circle

Equation of circle of radius R, center at (x₀,y₀)

(x - x₀)² + (y - y₀)² = R²

Equation of Circle of Radius R 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.