
Analytic Geometry
If the intersect curve of and are two lines
show that:
My idea is: joint the two equations:
then elimination one parameter: because is a plane, so
so let's Assume , then , take into in order to eliminate , we
get:
we know: it is a plane curve, and we know ,it replaces two plane lines if and only if :
where:
and I want to get the conclusion from : , But I failed, Help me :o

You have made a mistake here:
It should be
since the intersection are two lines, consider the above expression as a equation with y as unknown variable, simplify the equation by multiplying , its discriminant
must be a perfect square expression containning z as variable. that is to say,
is a perfect square expression with respect to z. thus its discriminant
which gives .