Question

If a + b + c = 0, then the family of lines 4ax + 3by + c = 0 are concurrent at __________.

Answer 1

Given a + b + c = 0
For family of lines, 4ax + 3by + c = 0
i.e. 4ax + 3by + (–a – b) = 0
i.e. a(4x − 1) + b(3y − 1) = 0
which passes through $x=\frac{1}{4}\mathrm{and}y=\frac{1}{3}$.