|
College
algebra contents E
|
|
|
|
|
|
|
|
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 y-axis |
Equation 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 |
|
|
|
|
|
|
|
|
College
algebra contents |
|
|
|
Copyright
© 2004 - 2020, Nabla Ltd. All rights reserved. |