Analytic Geometry - Conic Sections
Circle
General equation of a circle with the center S(p, q) - translated circle
The equation of the circle, example
Equation of the circle with the center at the origin O(0, 0)
Circle through three points
The equation of the circle through three points, example
Circle and Line
Line circle intersection
Circle and line examples
Equation of a tangent at a point of a circle with the center at the origin
Equation of a tangent at a point of a translated circle
Equation of a tangent at a point of a circle examples

Condition for a line to be the tangent to the circle with the center at the origin O(0, 0)
Condition for a line to be the tangent to the translated circle
Tangents to a circle from a point outside the circle - use of the tangency condition

Angle between two circles

Definition and construction

Constructions of an ellipse

The parametric equations of the ellipse

Equation of the tangent at a point on the ellipse

Equation of the hyperbola

Examining equation of the hyperbola

Equation of the hyperbola in vertex form

Examples of hyperbola

Translation of equilateral or rectangular hyperbola with the coordinate axes as its asymptote

Properties of the hyperbola
The area of a triangle which the tangent at a point on the hyperbola forms with asymptotes
The tangency point bisects the line segment of the tangent between asymptotes
The parallels to the asymptotes through the tangency point intersect asymptotes
The equation of the equilateral or rectangular hyperbola with the coordinate axes as its asymptotes
Hyperbola and line examples

of the parabola

Equation of a translated parabola - the standard form
Parametric equations of the parabola

Common points of a line and a parabola

The equation of the tangent and the normal at the point on the parabola
Properties of the parabola

Parabola and line examples

Conics, a Family of Similarly Shaped Curves - Properties of Conics
Conics, a Family of Similarly Shaped Curves – Properties of Conics

Conics - a family of similarly shaped curves