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Question: lines x + 2y – 1 = 0, ax + y + 3 = 0 and bx – y + 2 = 0 are concurrent and let S be the curve denoti...

lines x + 2y – 1 = 0, ax + y + 3 = 0 and bx – y + 2 = 0 are concurrent and let S be the curve denoting locus of (a, b). Then the least distance of S from the origin is.

A

557\frac { 5 } { \sqrt { 57 } }

B

551\frac { 5 } { \sqrt { 51 } }

C

558\frac { 5 } { \sqrt { 58 } }

D

559\frac { 5 } { \sqrt { 59 } }

Answer

558\frac { 5 } { \sqrt { 58 } }

Explanation

Solution

lines are concurrent

= 0

Ž 7b – 3a + 5 = 0

locus of (a, b) is 3x – 7y = 5

least distance from (0, 0) = length of perpendicular from (0, 0) =558= \frac { 5 } { \sqrt { 58 } }