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
15
B
25
C
15
D
23

Solution

## The correct option is A $$\dfrac {1}{\sqrt 5}$$$$y=e^{2x} + x^2$$At $$x=0 \Rightarrow y=1$$$$\displaystyle \frac{dy}{dx}=2e^{2x}+2x$$Slope of tangent at (0,1) $$=2$$Equation of tangent through (0,1) is$$y-1=2(x-0)$$$$\Rightarrow y-2x-1=0$$Distance of tangent from origin $$\displaystyle=|\frac{-1}{\sqrt{1+4}}|=\frac{1}{\sqrt{5}}$$Mathematics

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