Family OF straight line

Statement -1 : If a,b,c are parameters such that 3a + 2b+4c=0, then the family of lines ax +by+ c =0 pass through a fixed point (3,2). and Statement -2: The equation ax + by + c =0 wil represent a family of straight lines passing through a fixed point if there exist a linear relation between a, b and c.

Statement-1: All chords of the curve 3x^(2)-y^(2)-2x+4y=0 which subtend a right angle at the origin pass through a fixed point. Statement-2: The equation ax+by+c=0 represents a family of straight lines passing through a fixed point iff there is a linear relation between a, b and c.

Formula OF straight line

Various form OF straight line

Straight Line L2

Find the differential equation of the family of all straight lines.

Find the differential equation of the family of all straight lines passing through the origin.

Consider the family of lines 5x+3y-2 + lambda (3x-y-4)=0 and x-y+1 + mu (2x - y - 2) = 0 Equation of straight line that belong to both families is ax+by-7=0 then a+b is