The algebraic sum of distances of the line ax + by + 2 = 0 from ( 1,2 ), ( 2,1 ) and ( 3 , 5 ) is zero and the lines bx - ay + 4 = 0 and 3 x + 4 y + 5 = 0 cut the coordinate axes at concyclic points t

Question

The algebraic sum of distances of the line ax + by + 2 = 0 from ( 1,2 ), ( 2,1 ) and ( 3 , 5 ) is zero and the lines bx - ay + 4 = 0 and 3 x + 4 y + 5 = 0 cut the coordinate axes at concyclic points then

TestHub · Accepted Answer

Line always passes through the point ( 2 , 3 8 ​ ) hence 6 a + 8 b + 6 = 0 ⇒ 3 a + 4 b + 3 = 0 bx − ay + 4 = 0 and 3 x + 4 y + 5 = 0 are concyclic. So, m 1 ​ m 2 ​ = 1 a b ​ ⋅ − 4 3 ​ = 1 ⇒ 4 a + 3 b = 0 Solving a = 9/7 , b = − 12/7

Mathematics - Straight Lines Question with Solution | TestHub

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JEE Main - 1 year (12th class)