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If the linesx+y=2, 2x-y+1=0, px+qy=r are concurrent,then slope of member of the family 2px+3qy+4r=0which is farthest from origin

If the linesx+y=2, 2x-y+1=0, px+qy=r are concurrent,then slope of member of the family 2px+3qy+4r=0which is farthest from origin

Grade:12th pass

1 Answers

Harsh Patodia IIT Roorkee
askIITians Faculty 907 Points
6 years ago
concurrent lines solve x+y=2 and 2x-y+1=0 you get (1/3,5/3) now line px+qy=r will also pass through (1/3,5/3) so p/3+5q/3=r ,p+5q=3r.....(i)
2px+3qy+4r=0 distnace from origin is =4r/(4p2+9q2)1/2= now here put r and also put q/p =t and you will get (explained in image further)
228-1527_IMG-20180305-WA0102.jpg

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