| Analytic Geometry
- Conic
Sections |
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Circle |
General equation of a circle with the center
S(p, q) - translated circle |
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The
equation of the circle, example |
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Equation of the circle with the
center at the origin O(0, 0)
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Circle through three points
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The
equation of the circle
through three points,
example |
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Circle
and Line
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Line circle intersection
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Circle
and line examples
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Equation of a tangent at a point
of a circle with the center at the origin
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Equation of a tangent at a point
of a translated circle
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Equation of a tangent at a point
of a circle examples
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Condition of tangency - Condition for a line to be the tangent to a circle
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Condition for a line to be the tangent to the circle with
the center at the
origin
O(0, 0)
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Condition for a line to be the tangent to the translated circle
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Tangents to a circle from a point outside the circle - use of the
tangency condition
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Angle between a line and a circle
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Mutual position of two circles
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The radical line or the radical
axis
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The pole and the polar
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Angle between two circles
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Ellipse
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Definition and construction |
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Eccentricity and linear
eccentricity
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Constructions of an ellipse |
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Equation of the ellipse, standard
equation of the ellipse
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Major axis, minor
axis and
vertices
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The focal parameter, latus rectum
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The parametric equations of the ellipse |
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Equation of a translated ellipse
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Ellipse
and Line
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Intersection of ellipse and line - tangency condition
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Equation of the tangent at a point on the ellipse
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Construction of the tangent at a point on the ellipse
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Angle between the focal radii at a point of the ellipse
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Tangents to an ellipse from a
point outside the ellipse - use of the tangency condition
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Construction of tangents from a point outside the ellipse
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Polar and pole of the ellipse
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Equation of the polar of the given
point
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Ellipse and line examples
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Hyperbola
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Definition and construction
of the hyperbola
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Construction of the hyperbola
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Equation of the hyperbola
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Properties of the hyperbola
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Examining equation of the hyperbola
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Equilateral or rectangular
hyperbola
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Translated hyperbola
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Equation of the hyperbola in vertex form
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Parametric equation of the hyperbola
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Examples of hyperbola |
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Equilateral or rectangular hyperbola with the coordinate axes as its
asymptote
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Translation
of equilateral or rectangular hyperbola with the coordinate axes as its
asymptote |
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Hyperbola
and Line
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Hyperbola and line relationships
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Condition for a line to be the tangent to the hyperbola -
tangency condition |
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The equation of the tangent at the point on the hyperbola
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Polar and pole of the hyperbola
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Construction of the tangent at the point on the hyperbola
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Construction of tangents from a point outside the hyperbola
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Properties of the hyperbola
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The area of a triangle which the tangent at a point on the hyperbola forms with
asymptotes |
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The tangency point bisects the line
segment of the tangent between
asymptotes |
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The parallels to the asymptotes through the tangency point intersect asymptotes |
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The equation of the equilateral or rectangular hyperbola with the
coordinate axes as its
asymptotes |
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Hyperbola and line examples
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Parabola
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Definition and construction
of the parabola
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Construction of the parabola
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Vertex form of the equation of a parabola
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Transformation of the equation of a parabola
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Equation of a translated parabola - the standard form
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| The parabola whose axis
of symmetry is parallel to the y-axis |
| Equations of the parabola
written in the general form |
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Parametric equations of the parabola
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Parabola examples
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Parabola
and Line
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Common points of a line and a parabola |
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Condition for a line to be the tangent to the parabola
- tangency condition
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The equation of the tangent and the normal at the point on the parabola
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Properties of the parabola
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Polar of the parabola
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Construction of the tangent at the point on the parabola
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Construction of the tangents from a point exterior to the parabola
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Parabola and
line examples |
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Conics,
a Family of Similarly Shaped Curves - Properties of Conics |
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Conics,
a Family of Similarly Shaped Curves – Properties of Conics |
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Dandelin's
Spheres - proof of conic sections focal properties
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Proof that conic section curve is
the ellipse
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Proof that conic section curve is the hyperbola
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Proof that conic section curve is the parabola
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Conics - a family of similarly shaped curves |
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