The straight line L=x+y+1=0and L1x+2y+3=0 are intersecting. m is the slope of the straight line L2 such that L is the bisector of the angle between L1 and L2. The value of 812m2+3 is equal to
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Solution
Let the equation of L2 be L1+λL=0 ⇒(1+λ)x+(2+λ)y+3+λ=0 slopes of L2,L and L1 are −1+λ2+λ,−1,−1/2 Since L is the bisector of the angle between L1 & L2 ∴−1+λ2+λ+11+1+λ2+λ=−1+1/21+1/2⇒λ=−3 So the equation of L2 is y+2x=0⇒m=−2