I was studying about the straight lines in coordinate geometry and came across this topic named 'pair of straight lines'. It started in my book directly with "If we multiply the equation of two lines the resulting algebraic equation must be satisfied by the points on both the lines." I don't understand why we had to start this concept. What are the uses of this? And what does that two degree equation mean?
If you don't remember this concept here's something to remind you.
If we have two lines $p_1x+q_1y+r_1=0$ and $p_2x+q_2y+r_2=0$ then equation of pair of lines is given by $$(p_1x+q_1y+r_1)(p_2x+q_2y+r_2)=0$$ If we solve this equation we get a two degree equation in the form of $$ax^2+by^2+2hxy+2fx+2gy+c=0$$ Here is something to make you sure what I am talking about.
I assume this concept is equally applicable for conic sections. If I assume right then I hope there won't be much to discuss for them about their uses after discussing them for straight lines.
The general equation represents a pair of line if $abc+2fgh=af^2+bg^2+ch^2$ thus its a part of conics and with a homogeneous second degree equation you can find point of intersection of conic with a line using partial differentiation which is very short and nice method.