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Q.
Let the point P(α,β) be at a unit distance from each of the two lines L1:3x−4y+12=0, and L2:8x+6y+11=0. If P lies below L1 and above L2, then 100(α+β) is equal to
By observing origin and P lies in same region. L1(0,0)>0;L1(α,β)>0⇒3α−4β+12>01=|3α−4β+125| 3α−4β+12=5......(1)
Similarly for L2 L2(0,0)>0;L2(α,β)>0 1=|8α+6β+1110|⇒8α+6β+11=10.......(2)
Solving (1) and (2) α=−2325;β=106100 100(α+β)=100(−92100+106100)=14