83 The equation of common tangent to the parabola
Y2 2x and the hyperbola xy 4, is
(1) X+4Y+d-O
(2) 2x+2Y+ 1-0
(4) 8x 4y+1 = O
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@santosh
83.
Let us assume tangent be y=mx + b
General equation of tangent to parabola
is, y = mx + a/m
Also, general equation of tangent to rectangular hyperbola
on parametric point (ct,c/t) is, 
For common tangent,
Also,
Squaring both sides and substituting value of m as
Substituting value of c= 2 and a = 1/2,
=> m = -1/4
So equation of line is y = -x/4 - 2 which gives x+4y+8=0