Question

A curve passes through the point (2a, a) and is such that sum of subtangent and abscissa is equal to a. Its equation is

• A. $(x-a)y^2=a^3$
• B. $(x-a{)}^{2}y=a^3$
• C. $(x-a)y=a^2$
• D. $(x+a)y=a^2$

Answer 1

Answer: (C)

$(x-a)y=a^2$

$y-y=\frac{dy}{dx}(X-x)$
$\therefore$ coordinates of T are $(x-y\frac{dy}{dx},0)$
$\therefore$ sum of subtangent and abscissa $\equiv y\frac{dx}{dy}+x=a$
$\therefore$ $y\frac{dx}{dy}=a-x$
i.e. $\frac{dx}{a-x}=\frac{dy}{y}$
$\therefore$ $cy=\frac{1}{a-x}$
$\therefore$ $c=-\frac{1}{a^2}$
$\therefore$ equation of the curve is $(x-a)y=a^2$