# Screenshot_1330.png 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

@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

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