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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
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B
25
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C
15
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D
23
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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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