Question

Area of the triangle formed by the tangent at $x=2$ on the curve $y=\frac{8}{4+x^2}$ with the coordinate axes is (in sq. units)

• A. $4$
• B. $3$
• C. $2$
• D. $1$

Answer 1

The correct option is A $4$

$y=\frac{8}{4+x^2}$

$Atx=2y=1$

$y^{\prime }=\frac{-8\left(2x\right)}{(4+x^2{)}^2}=\frac{-16\times 2}{8^2}=\frac{-1}{2}$

Tangent is $y=mx+c$

$y=\frac{-1}{2}x+c$

passes through $(2,1)C=2$

$2y+x=4$

Base of triangle $=4$

Height of triangle $=\frac{4}{2}=2$

Area of $\Delta =\frac{1}{2}\times 4\times 2=4sq.unit$