Question

The value of m for which the area of the triangle included between the axes and any tangent to the $x^{m}y=b^m$ curve is constant, is

• A. $\frac{1}{2}$
• B. $1$
• C. $\frac{3}{2}$
• D. $2$

Answer 1

Answer: (B)

$1$

Given, $y=b^m{x}^{-m}$
$y^{\prime }=-b^m{x}^{-(m+1)}$
At any point $(x1,y1)$
Equation of tangent is given by
$\frac{y-y1}{x-x1}=-b^{m}x{1}^{-(m+1)}$
Y intercept $=-m$
X intercept $=(m-1)\times \frac{1}{m}$
Area bounded $=\frac{1}{2}\frac{(m-1)x1}{m}\times m$
For area to be constant, $m=1$