If the chord xcos⁡α+ysin⁡α−p=0 of the circle x2+y2−a2=0 subtends a right angle at the centre of the circle, thena2p2 is equal to

The combined equation of the lines joining the origin to the points of intersection of xcos⁡α+ysin⁡α=p and x2+y2−a2=0 is a homogeneous equation of second degree given by x2+y2−a2xcos⁡α+ysin⁡αp2=0⇒x2p2−a2cos2⁡α+y2p2−a2sin2⁡α−a2sin⁡2αxy=0The lines given by this equation are at right angle. Coeff. of x2+ Coeff. of y2=0 ⇒ p2−a2cos2⁡α+p2−a2sin2⁡α=0⇒2p2=a2