# If the line ax+y=c, touches both the curves x^2+y^2=1 and y^2=4squre root 2x, then mod c is equal to:

Solution:  Tangent on $\\ y^2=4\sqrt{2x}$ is $\\ yt=x+\sqrt{2}t^2$

As it is tangent on circle also,

$\\\Rightarrow \left | \sqrt{2}t^2/\sqrt{1+t^2} \right |=1\\ \\\Rightarrow 2t^4=1+t^2 ;ie;t^2=1$

Equation is $\\\pm y=x+\sqrt{2}$

hence $\\\left | c \right |=\sqrt{2}$

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