When two curves intersect they have the same x and y values This means that given the equations of the curves, we can solve them like simultaneous equations to find the points of intersection.
Example: Find the points of intersection of the curve
(1) and
(2).
The curve and the line are illustrated below.
We can put (1)=(2) to get
and multiply throughout by
to clear all the fractions.
Subtract 3 from both sides, factorise and solve.
so
or
Ifthen from (2)
and if
then from (2)