For a >0, let the curves C1:y2=ax and C2:x2= ay intersect at origin O and a point P .
Let the line x=b(0<b<a) intersect the chord OP and the x -axis at points Q and R ,
respectively. If the line x=b bisects the area bounded by the curves, C2 and C, and the area
of ΔOQR=12, then 'a' satisfies the equation:
x6+6x3-4=0
x6-12x3+4=0
x6-12x3-4=0
x6-6x3+4=0
∫0bax-x2adx=1216a4a43⇒2ab33-b33a=a26 Also b22=12⇒b=1∴2a3-13a=a264a=a2+2a⇒ 16a=a4+4a2+4a⇒ a6-12a3+4=0