AP EAMCET Engineering 22 Apr 2019 Shift 1 Paper

Consider the equations,
x+2y−5=0 ......(I)
3x−y+1=0 ......(II)
From equation (I) origin O and P are on same sides so, This implies,
(−5)(λ2+2λ−3 )>0
λ2+2λa−3<0
λ(λ+3)−1(λ+3)<0
(λ+3)(λ−1)<0
This gives,
λ∈(−3,1)
From equation (II),
(λ) (λ−

1

3

)>0
This gives,
λ∈(−∞,0)∪(

1

3

,∞)
{−2,−1}
Thus, there are two points.