Analytic geometry circle, General equation of circle with centre S(p, q), Translated circle, Equation of circle at origin, Equation of circle through three points example, Circle and line, Line circle intersection, Equation of tangent at point of circle with centre at origin, Equation of tangent at point of translated circle, Condition of tangency, Condition for line to be tangent to circle with centre at origin, Condition for line to be tangent to translated circle, Tangents to circle from point outside the circle, Use of tangency condition, Angle between line and circle, Radical line or radical axis, Pole and polar of circle, Angle between two circles, Ellipse, Definition of ellipse, Constructions of ellipse, Equation of ellipse, Standard equation of ellipse, Major axis of ellipse, Minor axis of ellipse, Vertices of ellipse, Focal parameter of ellipse, Latus rectum of ellipse, Parametric equation of ellipse, Equation of translated ellipse, Intersection of ellipse and line, Condition of tangency for ellipse, Equation of tangent at point on ellipse, Construction of tangent at point on ellipse, Angle between focal radii at point on ellipse, Tangents to ellipse from point outside ellipse, Construction of tangents from point outside ellipse, Polar and pole of ellipse, Equation of polar of ellipse of given point, Ellipse and line examples, Hyperbola, Definition of hyperbola, Construction of hyperbola, Equation of hyperbola, Properties of hyperbola, Examining equation of hyperbola, Equilateral or rectangular hyperbola, Translated hyperbola, Equation of hyperbola in vertex form, Parametric equation of hyperbola, Equilateral or rectangular hyperbola with coordinate axes as its asymptote, Hyperbola and line relationships, Condition for line to be tangent to hyperbola, Tangency condition for hyperbola, Equation of tangent at point on hyperbola, Polar and pole of hyperbola, Construction of tangent at point on hyperbola, Construction of tangent from point outside hyperbola, Area of triangle tangent at point on hyperbola forms with asymptotes, Tangency point bisects line segment of tangent between asymptotes, Parallels to asymptotes through tangency point intersect asymptotes, Equation of equilateral or rectangular hyperbola with coordinate axes as its asymptotes, Parabola, Definition of parabola, Construction of parabola, Vertex form of equation of parabola, Transformations of equations of parabola, Equation of translated parabola, Standard form of equation of parabola, Parabola whose axis of symmetry is parallel to y-axis, Equation of parabola in general form, Parametric equation of parabola, Common points of line and parabola, Condition for line to be tangent to parabola, Tangency condition for parabola, Equation of tangent and normal at point on parabola, Properties of parabola, Polar of parabola, Construction of tangent at point on parabola, Construction of tangents from point exterior to parabola, Conics family of similarly shaped curves, Properties of conics, Dandelin's spheres proof of conic sections focal properties, Proof that conic section is ellipse, Proof that conic section is hyperbola, Proof that conic section is parabola

Pre-calculus Contents H

Coordinate Geometry or 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 of tangency - Condition for a line to be the tangent to a circle

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 a line and a circle

Mutual position of two circles

The radical line or the radical axis

The pole and the polar of the circle

Angle between two circles

Ellipse

Definition and construction of an ellipse

Eccentricity and linear eccentricity

Constructions of an ellipse

Equation of the ellipse, standard equation of the ellipse

Major axis, minor axis, and vertices

The focal parameter, latus rectum

The parametric equations of the ellipse

Equation of a translated ellipse

Ellipse and Line

Intersection of ellipse and line - tangency condition

Equation of the tangent at a point on the ellipse

Construction of the tangent at a point on the ellipse

Angle between the focal radii at a point of the ellipse

Tangents to an ellipse from a point outside the ellipse - use of the tangency condition

Construction of tangents from a point outside the ellipse

Polar and pole of the ellipse

Equation of the polar of the given point

Ellipse and line examples

Hyperbola

Definition and construction of the hyperbola

Construction of the hyperbola

Equation of the hyperbola

Properties of the hyperbola

Examining equation of the hyperbola

Equilateral or rectangular hyperbola

Translated hyperbola

Equation of the hyperbola in vertex form

Parametric equations of the hyperbola

Examples of hyperbola

Equilateral or rectangular hyperbola with the coordinate axes as its asymptote

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

Hyperbola and line

Hyperbola and line relationships

Condition for a line to be the tangent to the hyperbola - tangency condition

The equation of the tangent at the point on the hyperbola

Polar and pole of the hyperbola

Construction of the tangent at the point on the hyperbola

Construction of tangents from a point outside the hyperbola

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

Parabola

Definition and construction of the parabola

Construction of the parabola

Vertex form of the equation of a parabola

Transformation of the equation of a parabola

Equation of a translated parabola - the standard form

The parabola whose axis of symmetry is parallel to the y-axis

Equations of the parabola written in the general form

Parametric equations of the parabola

Examples of the parabola

Parabola and line

Common points of a line and a parabola

Condition for a line to be the tangent to the parabola - tangency condition

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

Properties of the parabola

Polar of the parabola

Construction of the tangent at the point on the parabola

Construction of the tangents from a point exterior to 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

Dandelin's Spheres - proof of conic sections focal properties

Proof that conic section curve is the ellipse

Proof that conic section curve is the hyperbola

Proof that conic section curve is the parabola

Conics - a family of similarly shaped curves

Pre-calculus Contents