Equation of the curve whose sub tangent is constant is

y^{2} = c e^{\frac{x^{2}}{k}}

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y = c x^{2}

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y = c e^{\frac{x}{k}}

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y = c e^{x^{2}}

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Solution

The correct option is B $y = c e^{\frac{x}{k}}$
Given,sub tangent, $T N =$ constant (lets say it as $k$ )
$\Rightarrow y c o t ϕ = k$
But Slope, $t a n ϕ = \frac{d y}{d x}$
$\Rightarrow y * \frac{d x}{d y} = k$
$\Rightarrow k * \frac{d y}{y} = d x$
On integrating once,
$\Rightarrow \int (k * \frac{d y}{y}) = \int d x$
$\Rightarrow k * l n y = x$
$\Rightarrow y = c e^{\frac{x}{k}}$

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Equation of the curve whose sub tangent is constant is

The correct option is B y=cexkGiven,sub tangent,TN=constant (lets say it as k)⇒ycotϕ=kBut Slope,tanϕ=dydx⇒y∗dxdy=k⇒k∗dyy=dxOn integrating once,⇒∫(k∗dyy)=∫dx⇒k∗lny=x⇒y=cexk