An interesting fact I thought about today. Let us suppose we have to determine the points of intersection of the cartesian equations and
. What we generally do is
.
Why? Because the points of intersection will, on substitution, make both sides equal. On substitution, the values obtained on both sides will be
.
But does the equation only determine the points of intersection of the figures
and
? No. It also determines the points of intersection of the figures
and
for every
.
Shocking, isn’t it? Determining only the points of intersection relevant to can be done by substitution of the points obtained in the two equations separately.