x-2y+4=0 is a common tangent to y2=4x & x24+y2b2=1 Then the value of b and the other common tangent are given by:

x-2y+4=0is a tangent to  x24+y2b2=1⇒a2l2+b2m2=n2⇒4+b2(4)=16⇒b2=3The other tangent must be reflection of x-2y+4 = 0 in the x-axis since both curves are symmetrical about x-axis.x+2y+4=0 is the other common tangent.