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

$2\sqrt{3}$ $2/\sqrt{5}$ $2/\sqrt{7}$ None of these

$2/\sqrt{5}$

$y=e^{2x}+x^2⇒\frac{dy}{dx}|_{x=0}=2×e^0+2×0=2$ So slope of normal = $-\frac{1}{2}$ Equation of normal is $y-1=-\frac{1}{2}(x-0)⇒x+2y-2=0$ Distance from origin = $\frac{2}{\sqrt{5}}$