Fewpal
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The straight line 2x + 3y + 1= 0 bisects the angle between two straight lines of which one line is 3x + 2y + 4 = 0. Then, the equation of the other line is

(A) 9x + 26y = 48

(B)  9x + 46y = 28

(C)  9x + 26y = 28

(D)  3x + 26y = 48

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Best answer

Correct option (B)  9x + 46y = 28

Explanation :

See Fig. Let L1  3x + 2y + 4 = 0, L ≡ 2x + 3y + 1 = 0 and L2  0 be the required lines. Since the line L2  0 passes through the intersection of the lines L 0, and L2 = 0

 Suppose (α,β) ( the intersection of L1 = 0 and L1 = 0 and L = 0) is a point on the L = 0 so that

2α + 3β + 1 = 0  ....(1)

But L = 0 is an angular bisection of L1 = 0 and L2 = 0 which implies that

Therefore, λ = 0 gives the line L1 = 0 and λ = -24/13 gives the line

 Therefore, the required line is L2 9x + 46y - 28 = 0.

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