Question

Area of the triangle formed by the normal to the curve $x=e^{\sin y}$ at (1, 0) with the coordinate axes is

• A. $\frac{1}{4}$
• B. $\frac{1}{2}$
• C. $\frac{3}{4}$
• D. $1$

Answer 1

Answer: (B)

$\frac{1}{2}$

$x=e^{\sin y}$

On differentiating

$\frac{1}{x}=y^{\prime }cosy$

$y^{\prime }=1$

$\therefore$ Slope of normal$=-1$

$(y-0)=-1(x-1)$

$y=1-x$

Area $=\frac{1}{2}\times 1\times 1$$=\frac{1}{2}$