if a^2 + b^2 - c^2 - 2ab = 0 , then family of st. lines ax+by+c=0 intersects at which point(s)?

Rearranging:-

a²-2ab+b²=c²

(a-b)²=c²

c=a-b

Now,

ax+by+c=0

ax+by+(a-b)=0 (as c=a-b)

ax+a+by-b=0

a(x+1)+b(y-1)=0

To satify this equation, (x+1) and (y-1) must be zero,

So, x+1=0 and y-1=0

x=-1 and y=1

So it will intersect at point (-1,1)