A Level Maths Notes: FP2 – The Parabola
A parabola is the locus of points defined by the condition that
the the distance from a point on the curve to a fixed point F is
equal to the least distance from that point on the line to a fixed
line L:
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The point F is called the focus.
The point L is called the directrix.
If the points
have
coordinates
respectively
then the distance
and![]()
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This equation of for a vertex at the origin If the vertex is at
the point
and
the curve oriented above then
In
general the parabola may be scaled, translated and rotated. The most
general equation of an parabola is
with
the condition that
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