A and B are two points on the hyperbola x2a2−y2b2=1 O is the centre. If OA is perpendicular to OB then 1(OA)2+1(OB)2 is equal to

Let OA=r1 and the coordinates of A be r1cos⁡α,r1sin⁡αr2cos⁡α+π2,r2sin⁡α+π2As A, B lie on the hyperbola x2a2−y2b2=1r12cos2⁡αa2−sin2⁡αb2=1r22sin2⁡αa2−cos2⁡αb2=1⇒1(OA)2+1(OB)2=1r12+1r22=1a2−1b2.