Question

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

• A. $\frac{1}{\sqrt{5}}$
• B. $\frac{2}{\sqrt{5}}$
• C. $\frac{1}{\sqrt{3}}$
• D. $\frac{2}{\sqrt{3}}$

Answer 1

The correct option is A $\frac{1}{\sqrt{5}}$

Point on curve $(0,1)$.
$\frac{dy}{dx}=2e^{2x}+2x$
at $(0,1)$ slope of tangent $=2$
The equation of the tangent at $(0,1)$ is

$y-1=2(x-0)$
$2x-y+1=0\cdots \left(1\right)$
Distance from origin to line $=\frac{2\left(0\right)-0+1}{\sqrt{4+1}}$
$\therefore$ Required distance is $\frac{1}{\sqrt{5}}$ units.