If ab+bc+ca=0,show that the lines x/a+y/b=1/c,x/b+y/c=1/a and x/c+y/a=1/b are concurrent?
2 Answers
See below.
Explanation:
If
Given the Matrix
if the three lines represented have a common point then their coefficients are linearly dependent and then
but
and as we can observe this relationship is true if
Let the point of intersection of two straight lines
So
and
Adding [3] and [4] we get
But the given condition is
Dividing both sides by
Combining {5}and [6] we get
The relation [7] is only possible iff
Hence we can say that the given three straight lines are concurrent under given condition