The three ellipses x2ai2+y2bi2=1,i=1,2,3, have a common tangent, then the value of a12    b12    1a22    b22    1a32    b32    1=

Let the common tangent be y=mx+c⇒ Point of tangencies to the given ellipses are −a12mc,b12c,−a22mc,b22c,−a32mc,b32c Which are collinear ⇒−a12mcb12c1−a22mcb22c1−a32mcb32c1=0