Explanation

(c)
Let the point of contact be $(x_{1},\ y_{1})$
The equation of curve is
$\frac{x^{n}}{a^{n}} + \frac{y^{n}}{b^{n}} = 2$
$\Rightarrow \ \ \ \ \ \left( \frac{dy}{dx} \right)_{(x_{1},\ y_{1})} = - \frac{b^{n}}{a^{n}}\ .\frac{x_{1}^{n - 1}}{y_{1}^{n - 1}}$ ...(i)
The equation of line is $\frac{x}{a} + \frac{y}{b} = 2$
$\Rightarrow \ \ \ \ \ \ \ \left( \frac{dy}{dx} \right)_{(x_{1},\ y_{1})} = - \frac{b}{a}$ ...(ii)
From Eqs. (i) and (ii), we get
$- \frac{b}{a} = - \frac{b^{n}}{a^{n}}\ .\frac{x_{1}^{n - 1}}{y_{1}^{n - 1}}\ \ \ \ \ \Rightarrow \ \ \ \ \ \ x_{1} = \frac{ay_{1}}{b}$ ...(iii)
Also, $(x_{1},\ y_{1})$ lies on the given line
$\therefore\ \ \ \frac{ay_{1}}{ab} + \frac{y_{1}}{b} = 2$
$\Rightarrow \ \ \ \ \ \ \ \ y_{1} = b$ and $x_{1} = a$