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

\frac{1}{2}

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1

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\frac{3}{2}

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2

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Solution

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

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