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Desired equation of pair of lines passing through (2, -1) is :

solving equation 1 and 2, we get:

============================= Alternately,

The lines are L1 = y - m₁ x - c₁ = 0 and y - m₂ x - c₂ = 0

These two lines pass through the point (2, -1) c₁ = -1 -2m₁ and c₂ = -1 - 2 m₂

multiply these equations and compare with the standard form of equation of pair of straight lines, we get

2 g = m₁ c₂ + m₂ c₁ , 2 f = - (c₁ + c₂ ) and c = c₁ c₂