If $a^2 +b^2-c^2-2ab=0$, then find line of the point(s) of concurrency of family of straight lines $ax+by+c=0$.

Given: $a^2 +b^2-c^2-2ab=0$

To do: To find line of the point(s) of concurrency of family of straight lines $ax+by+c=0$.

Solution:

As given, $a^2+b^2-c^2-2ab=0$

$\Rightarrow a^2+b^2-2ab-c^2=0$

$\Rightarrow ( a-b)^2-c^2=0$

$\Rightarrow ( a-b-c)( a-b+c)=0$

$\Rightarrow a=b+c\ and\ b=a+c$

On substituting this in equation $ax+by+c=0$,

$\Rightarrow ( b+c)x+by+c=0$

$\Rightarrow bx+cx+by+c=0$

$\Rightarrow  b( x+y)+c(x+1)=0$

To satisfy the equation, $x+y=0$ and $x+1=0$,

$\Rightarrow x=-y\ or\ x=-1$

Tutorialspoint

e

Updated on: 10-Oct-2022

20 Views

Kickstart Your Career

Get certified by completing the course

Get Started