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Q)

Find all curves in x-y plane such that tangent at each point (x,y) of curves intersects the x-axis at $(x-1,0)$

$(a)\;y= ce^{2x} \\ (b)\;y=e^{2x}+c \\ (c)\;y= e^x+c \\ (d)\;y=ce^{x} $

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A)
Let slope of tangent =$\large\frac{dy}{dx}$
So, equation of the tangent passing through $(x-1,0)$ is
$y-0=\large\frac{dy}{dx}$$(x-x+1)$
$dx= \large\frac{dy}{y}$
$\log y =x + \log c$
$y= ce^x$
Hence d is the correct answer.
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