Question

Verify that the equation of a line passing through the point of intersection of two lines alx + bly + c1 = 0 and a2x + b2y + c2 = 0 is in the form (a1x + bly + c1) + K (a2x + b2y + c2) = 0.​

Answer 1

if both the lines are perpendicular then, m1m2=−1

m1,m2 are slopes of lines,

m1=a1−b1

m2=a2−b2

m1m2=−1

a1a2b1b2=−1

b1b2=−a1a2

a1a2+b1b2=0