Question

Length of the subtangent at $(a,a)$ on the curve $y^2=\frac{x^2}{2a+x}$ is equal to

• A. $\frac{18}{5}$
• B. $\frac{18a}{5}$
• C. $-\frac{18a^2}{5}$
• D. $\frac{18a^2}{5}$

Answer 1

Answer: (D)

$\frac{18a^2}{5}$

length of subtangent is $y\frac{dx}{dy}$
$y^2=\frac{x^2}{2a+x}2y.\frac{dy}{dx}=\frac{(2a+x)2x-x^2}{(2a+x{)}^2}\therefore \frac{dx}{dy}=\frac{2y.(2a+x{)}^2}{(2a+x)2x-x^2}$
$at(a,a)\frac{dx}{dy}=\frac{18a^3}{5a^2}=\frac{18a}{5}$
length of subtangent is $y\frac{dx}{dy}=a\times \frac{18a}{5}=\frac{18a^2}{5}$