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Question

The equation of the straight line passing through the point of intersection of the straight linesxa=yb=1 and xb+ya=1 and having infinite slopes is

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Solution

Let L1:xa+yb1=0 & L2=xb+ya1=0

the required line would be of the form L1λL2=0

(xa+yb1)λ(xb+ya1)=0

x(1aλb)+y(1bλa)1+λ=0

As slope = line is parallel to y-axis

coeff. of y=0λa=1bλ=ab

Eqn of line : x(1aab2)+y(1b1b)1+ab=0

x(b2a2ab2)+ab1=0

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