# 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 $y^2 = 4ax$ is, y = mx + a/m

Also, general equation of tangent to rectangular hyperbola $xy = c^2$ on parametric point (ct,c/t) is, $y = -\frac{x}{t^2} +\frac{2c}{t}$

For common tangent,

$m= \frac{-1}{t^2}$

Also, $b= \frac{2c}{t}= \frac{a}{m}$

Squaring both sides and substituting value of m as $m= \frac{-1}{t^2}$

$=> -4c^2 m = \frac{a^2}{m^2}$

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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