1. ©G Dear2008 – Not to be sold/Free to use
Mathematic
(Preliminary)
Locus and
the Parabola
Harder Parabolas
Stage 6 - Year 11
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©G Dear2008 – Not to be sold/Free to use

2. Parabola as a locus Vertex is at (h, k) Focus is at (h, k+a)
The parabola, vertex (h, k) and focal length a,
has the equation (x – h)2 = 4a(y – k).
Vertex is at (h, k)
x = h
(h, k + a)
Focus is at (h, k+a) a
Focal Length a
(h, k)
Axis is x = h
Directrix is y = k-a
y = k -a

3. Parabola as a locus
Find the equation of the parabola with focus (2,3) and with directrix y =-7.
a =(3 + 7)/2 = 5
Vertex = (2,3-5) = (2,-2)
= (h, k)
(2, 3)
a=5
(x – h)2 = 4a(y – k)
(x – 2)2 = 4(5)(y – -2)
(2, -2)
x2 – 4x + 4 = 20 (y + 2)
x2 – 4x + 4 = 20y + 40
y -7
x2–4x-20y-36=0