Question

The area of the triangle formed by tangent of the curve $y=\frac{8}{4+x^2}$ at x =2 on it and the axes is:

• A. 2 sq. units
• B. 4 sq. units
• C. 8 sq. units
• D. 16 sq. units

Answer 1

The correct option is B 4 sq. units

Given, $y=\frac{8}{4+x^2}$, when $x=2$, $y=1$

$\frac{dy}{dx}=\frac{-8.2x}{(4+x^2{)}^2}=\frac{-16x}{(x^2+4{)}^2}$

$\Rightarrow {\frac{dy}{dx}|}_{x=2}=\frac{-16\left(2\right)}{8^2}=\frac{-1}{2}$ …….$\left(1\right)$

Equation of tangent: $\frac{y-1}{x-2}=\frac{-1}{2}$

$\Rightarrow 2(y-1)+x-2=0$

$x+2y=4$

In intercept form, $\frac{x}{4}+\frac{y}{2}=1$

Area of triangle$=\frac{1}{2}\left(4\right)\left(2\right)=4$ sq. units

$\therefore$ Option B is correct.