If the tangents to ${\mathrm{y}}^2=2\mathrm{x}$ at 3 points have inclinations 30°, 40°, 50° and the ordinates of corresponding points are ${\mathrm{y}}_1,{\mathrm{y}}_2,{\mathrm{y}}_3$ then the ascending order of ${\mathrm{y}}_1,{\mathrm{y}}_2,{\mathrm{y}}_3$ is

$$\begin{gathered} \mathrm{Given} \mathrm{parabola} {\mathrm{y}}^2=2\mathrm{x} \\ \Rightarrow 4\mathrm{a}=2\Rightarrow \mathrm{a}=\frac{1}{2} \\ \mathrm{Equation} \mathrm{of} \mathrm{tangent} \mathrm{at} \text{'}\mathrm{t}\text{'} \mathrm{is} \mathrm{yt}=\mathrm{x}+{\mathrm{at}}^2 \\ \mathrm{slope} \mathrm{of} \mathrm{tangent}=\frac{1}{\mathrm{t}}\Rightarrow \mathrm{t}=\mathrm{cot\theta } \\ \mathrm{Let} {\mathrm{t}}_1,{\mathrm{t}}_2,{\mathrm{t}}_{3 } \mathrm{be} \mathrm{ordinates} \mathrm{of} \mathrm{the} \mathrm{three} \mathrm{points} \mathrm{then} {\mathrm{y}}_1={\mathrm{t}}_1,{\mathrm{y}}_2={\mathrm{t}}_2,{\mathrm{y}}_3={\mathrm{t}}_3 \\ \mathrm{Given} \mathrm{inclinations} \mathrm{of} \mathrm{tangents} \mathrm{are} {\mathrm{\theta }}_1={30}^0 ,{\mathrm{\theta }}_2={40}^0, {\mathrm{\theta }}_3={50}^0 \\ Since cot{50}^0<cot{40}^0<cot{30}^0 then {\mathrm{y}}_3<{\mathrm{y}}_2<{\mathrm{y}}_1 \\ \Rightarrow {\mathrm{y}}_3<{\mathrm{y}}_2<{\mathrm{y}}_1 \\ \mathrm{So} \mathrm{ascending} \mathrm{order} \mathrm{of} \mathrm{ordinates} \mathrm{is} {\mathrm{y}}_3,{\mathrm{y}}_2,{\mathrm{y}}_1 \end{gathered}$$

Ordinates are ${\mathrm{y}}_1, {\mathrm{y}}_2, {\mathrm{y}}_3$