Parabola

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Parabola
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Parabola

• A parabola is the set of all points (x,y) that
  are equidistant from a fixed line(directrix) and
  a fixed point (focus) not on the line.

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Standard Equation of a Parabola

• The standard form of the equation of a parabola
  with vertex at (h,k) is as follows.

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The midpoint between the focus and the directrix
is called the vertex, and the line passing
through the focus and the vertex is called the
axis of the parabola.
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• The focus lies on the axis p units (directed
  distance) from the vertex. If the vertex is at
  the origin(0,0), the equation takes one of the
  following forms.

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Length of the Latus Rectum

• Latus Rectum is the segment perpendicular to the
  axis of symmetry passing through the focus. The
  latus rectum has endpoints on the parabola.

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Parabola of the form

• Pgt0, opens upwards
• plt0, opens downwards
• Axis (of symmetry) x h
• Vertex (h,k)
• Focus (h,kp)
• Directrix y k-p
• Latus Rectum

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Parabola of the form

• Pgt0, opens right
• plt0, opens left
• Axis (of symmetry) y k
• Vertex (h,k)
• Focus (hp,k)
• Directrix x h-p
• Latus Rectum