Question

The sub-tangent at any point of the curve $x^m.y^n=a^{m+n}$ varies as

• A. $(abscissa{)}^2$
• B. $(abscissa{)}^3$
• C. $abscissa$
• D. $(ordinate{)}^2$

Answer 1

Answer: (C)

$abscissa$

$x^m.y^n=a^{m+n}$
$\Rightarrow mlogx+nlogy=(m+n)loga$
$\Rightarrow \frac{m}{x}+\frac{n}{y}.\frac{dy}{dx}=0$
$\Rightarrow \frac{dy}{dx}=\frac{-my}{nx}$
$\therefore sub-tangent=\left|\frac{y}{m}\right|=\frac{nx}{m}=\frac{n}{m}.x$
$\Rightarrow$ propotional to 'x'