Activities

Conic sections - parabola - cartesian equation in standard form

As an alternative to the locus method, it is often easier to use the standard form of the equation:

y2 = 4ax    or    x2 = 4ay

The standard form of the equation for the parabola assumes that:

  • the vertex is at the origin
  • the directrix is parallel to the x-axis or the y-axis.
    • See p98-99 QMaths12C and diagrams.

    When the vertex is not at the origin, the standard form can be adjusted to allow for translations (example).

    Attempt problems 1, 2, 3, 4 in Ex 3.2 p103 QMaths12C.
    In problem 4, complete the square to write the equation in the form:
    (y - k)2 = 4a(x - h)      or      (x - h)2 = 4a(y - k)      [N.B. The vertex is at the point (h,k).]