CONIC SECTIONS

CONIC SECTIONS

1. the curves which result from the intersection of a plane with a cone

2. PARABOLA

   • DEFINITION
     • a curve where any point is at an equal distance from a fixed point(focus) and a fixed straight line(directrix)
   • ELEMENTS
     • Vertex- a point that changes the direction of the parabola.
       • Focus- a fixed point used to define the parabola. Located inside the parabola
         • Focal Length- the length between the vertex and the focus
           • Latus Rectum- a line perpendicular to the line joining the vertex and the focus. It is 4x the length of the focal length
             • Directrix- a straight line in front of the parabola.
               • Axis- a line perpendicular to the directrix
   • FORMULA
     • y= a (x-h)^2+k
   • EXAMPLES

3. CIRCLE

   • ELEMENTS
     • Circumference, Radius, Diameter, Chord, Tangent, Secant, Arc, Segment, Sector
   • DEFINITION
     • A closed, two- dimensional curved shape.
   • FORMULA
     • Diameter of a Circle D = 2 × r
       • Circumference of a Circle C = 2 × π × r
         • Area of a Circle A = π × r2
   • EXAMPLE

4. ELLIPSE

   • ELEMENTS
     • Foci, Major Axis, Minor Axis, Center, Facal length, Vertices, Convertices, Semi-minor Axis, Semi-major Axis
   • DEFINITION
     • Is a set of all points on an XY-plane, which the distance from two fixed points adds up to a constant value.
   • FORMULA
     • Ax^2+Cy^2+Dx+Ey+F=0
   • EXAMPLES

5. HYPERBOLA

   • DEFINITON
     • two-branched open curve, a conic section, produced by the intersection of a circular cone and a plane that cuts both nappes of the cone.
   • EXAMPLES
   • FORMULA
     • Ax^2+Cy^2+Dx+Ey+F=0
       • (x-h)^2/a-(y-k)^2/b=1
   • ELEMENTS
     • Foci, Transverse axis, Conjugate axis, Semi-major axis, Semi-minor axis, Center Vertices, Focal length, Axes of symmetry, Asymptotes

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