Question

Find the equations to the straight lines passing through the pairs of points. : $(a,b)$ and $(a+b,a-b)$.

Answer 1

Given points are $(a,b)$ and $(a+b,a-b)$

Then, equation of line is

$y-b=\frac{a-b-b}{a+b-a}\times (x-a)$

$\Rightarrow b(y-b)=(x-a)\times (a-2b)$

$by-b^2=ax-2bx-a^2+2ab$

Therefore required equation is

$(a-2b)x-by+b^2+2ab-a^2=0$