If the point $P(a^2,a)$ lies in the region corresponding to the acute angles between the lines $2y=x$ and $4y=x$ then range of a is...
This would have been easy if the lines had constants and I can see the position of point with respect to origin but now both the lines pass through the origin.
Hint:
(Large version)
What is the allowed region for points $P$, where $P = (a^2, a)$ for some real $a$?
What is the equation of the curve where all $P$ reside on?
Which $P$ are within the allowed region?
What are the $a$ values of these points?