Find the angle subtended by the double ordinate of length 2a of the parabola y2 = ax at its vertex

let the parabola be the given as in diagram

vertex--O and QQ^' ---DOUBLE ORDINATE

parabola is y²=ax
y=±√ax

thus coordinates of Q and Q^' is (x,√ax
) and (x,-√ax) respectively

but length of double ordinate =2a
thus QQ^'=2a

2√ax=2a
x=√a
from given figure i.e right angled triangle tanθ=√a

thus total angle subtended by the double ordinate at vetex is 2tan^-1√a