Explanation

(d)
Given curve is $x^{2} + xy + y^{2} = 7$
$\Rightarrow \ \ \ \ \ \ \ 2x + x\frac{dy}{dx} + y + 2y\frac{dy}{dx} = 0$
$\Rightarrow \ \ \ \ \ \ \ \frac{dy}{dx} = - \frac{(2x + y)}{x + 2y}$
$\Rightarrow \ \ \ \ \ \ \left( \frac{dy}{dx} \right)_{(1,\ - 3)} = \frac{- (2 - 3)}{(1 - 6)} = - \frac{1}{5}$
$\therefore$ Length of subtangent$= \frac{y}{\frac{dy}{dx}} = \frac{- 3}{\frac{1}{- 5}} = 15$