The range of λ if the point (λ, λ+1) lies inside the parabola y2=14x
(12−√1402,12+√1402)
(14−√1902,14+√1902)
(6,8)
(12−√1402,14+√1902)
The point (x1,y1) lies inside y2−14x=0 if y21−14x1 < 0
⇒ (λ+1)2−14 λ < 0
⇒ λ2+2λ+1−14λ
⇒ λ2−12λ+1 < 0
λ∈(12−√122−42,12+√122−42)
=(12−√1402,12+√1402)