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
 
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