The point (λ,λ−2) lies inside the ellipse ‌4x2+9y2=36 ‌⇒‌‌4λ2+9(λ−2)2<36 ‌⇒‌‌4λ2+9λ2+36−36λ<36 ‌⇒‌‌13λ2−36λ<0 ‌⇒‌‌(13λ−36)<0 ‌⇒‌‌0<λ<‌
36
13
....(i) The point (λ,λ−2) also lies outside the parabola y2=x ‌(λ−2)2−λ>0