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

O(0, 0)

The pole and the polar of the circle

Definition and construction of an ellipse

Constructions of an ellipse

The parametric equations of the ellipse
Equation of a translated ellipse
Ellipse and Line

Equation of the tangent at a point on the ellipse

Equation of the hyperbola

Equilateral or rectangular hyperbola

Examples of hyperbola

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

Hyperbola and line relationships

Polar and pole 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

Definition and construction of the parabola

Parabola and line
Common points of a line and a 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

Proof that conic section curve is the ellipse
Proof that conic section curve is the hyperbola

Pre-calculus Contents