The variable coefficient p,q,r in the equation of the straight line px+qy+r=0 are connected by the relation pa+qb+rc=0 where a,b and c are fixed contants.show that the variable line always passes through a fixed point?
2 Answers
See below.
Explanation:
Solving
for
which is the intersection point.
Solving now
for
substituting now the values found to
so as we can conclude all the lines have a common point with coordinates
Given that the equation
We are to show that the variable line always passes through a fixed point.
Given equation of variable straight line
Given relation
Dividing both sides of the given relation by
It is obvious from equation [1] and [3] that equation [3] is possible when the variable straight line passes through the fixed point