A Level Maths Notes: FP1 – Finding the Equations of Tangents and Normals to Parametric Curves
Parametric curves take the
form
where
is
a parameter. Each value of
gives (not necessarily unique) values of
and
If
we need to find the equation of a tangent or normal to the curve at
any point
then
we need the gradient
at
that point. We find
using
the identity
will
be a function ofso
if we have the vale of
we
can find
the
coordinatesthen
use
to
find the equation of the tangent or
to
find the equation of the normal.
Example: Find the equation
of the tangent and normal for the curve given in parametric
coordinates as
at
At
Tangent:
Normal:
If we have the point
but
not
then
we have to use the point to find
Example: Find the equation
of the tangent and normal for the curve given in parametric
coordinates as
at
the point
We have to find the value
of
and
From
these two,
Tangent:
Normal: