The curves


The curves $y=a e^{x}$ and $y=b e^{-x}$ cut orthogonally, if

A. $a=b$

B. $a=-b$

C. $a b=1$

D. $a b=2$


Given that the curves $y=a e^{x}$ and $y=b e^{-x}$

Differentiating both of them w.r.t. $x$,

$\frac{\mathrm{dy}}{\mathrm{dx}}=\mathrm{ae}^{\mathrm{x}}$ and $\frac{\mathrm{dy}}{\mathrm{dx}}=-\mathrm{be}^{-\mathrm{x}}$

Let $m_{1}=a e^{x}$ and $m_{2}=-b e^{-x}$

$\mathrm{m}_{1} \times \mathrm{m}_{2}=-1$

(Because curves cut each other orthogonally)

$\Rightarrow-a b=-1$

$\Rightarrow a b=1$

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