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The distance between the origin and the tangent to the curve $y = e^{2 x} + x^{2}$ drawn at the point $x = 0$ is

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$\frac{1}{\sqrt{5}}$

$\frac{2}{\sqrt{5}}$

$\frac{- 1}{\sqrt{5}}$

$\frac{2}{\sqrt{3}}$

answer is A.

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Detailed Solution

Point on curve (0,1) The equation of the tangent at (0,1) is 2x-y+1=0....(1) Required distance = $\frac{1}{\sqrt{5}}$

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