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$If \frac{x}{c} + \frac{y}{d} = 1 be any line through the intersection of lines \frac{x}{a} + \frac{y}{b} = 1 and \frac{x}{b} + \frac{y}{a} = 1, then$

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1a+1d=1b+1c

1b+1d=1c+1a

1c+1d=1a+1b

a+b=c+d

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detailed solution

Correct option is C

Point of intersection of xa+yb=1 and xa+ya=1 is aba+b,aba+bPutting the point in xc+yb=1, we get 1c+1d=1a+1b

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If xc+yd=1 be any line through the intersection of lines xa+yb=1 and xb+ya=1 , then

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$If \frac{x}{c} + \frac{y}{d} = 1 be any line through the intersection of lines \frac{x}{a} + \frac{y}{b} = 1 and \frac{x}{b} + \frac{y}{a} = 1, then$