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

Angle between two circles

Ellipse

Definition and construction 
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 equation 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 yaxis 
Equations of the parabola
written in the general form 
Parametric equations of the parabola

Parabola examples

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 










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