Question

The value of m for which the area of the triangle included

between the axes and any tangent to the curve x^my = b^m is

constant, is –

• A. ½
• B. 1
• C. 3/2
• D. 2

Answer 1

Answer: (B)

1

Answer 2

For x^m. y = b^m

$\frac{dy}{dx}$= – $\frac{my}{x}$Ž EOT Ž y – y₁ = $\frac{–my_{1}}{x_{1}}$ (x – x₁)

Ž y + $\frac{my_{1}}{x_{1}}$x = y₁ + my₁ Ž $\frac{x}{x_{1} + \frac{x_{1}}{m}}$+ $\frac{y}{(y_{1} + my_{1})}$ = 1

Area of D = $\frac { 1 } { 2 }$ $\left( x_{1} + \frac{x_{1}}{m} \right)$ (y₁ + my₁) = $\frac{xy(1 + m)^{2}}{2m}$

= $\frac{b^{m}(1 + m)^{2}}{2mx^{m–1}}$= constant for m = 1