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$I f p i s t h e l e n g t h o f t h e p e r p e n d i c u l a r f r o m t h e o r i g i n t o t h e l i n e \frac{x}{a} + \frac{y}{b} = 1 t h e n$

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1a2+1b2=1p2

1a2+1b2=2p2

1a2-1b2=1p2

1a2+1b2=p2

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Correct option is A

The perpendicular distance from origin to the line ax +by +c=0 is ca2+b2 The distance from origin to the line xa+yb=1 is p, given p=11a2+1b2take reciprocals and then squaring both sides1a2+1b2=1p2

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If p is the length of the perpendicular from the origin to the line xa+yb=1 then

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$I f p i s t h e l e n g t h o f t h e p e r p e n d i c u l a r f r o m t h e o r i g i n t o t h e l i n e \frac{x}{a} + \frac{y}{b} = 1 t h e n$