Let a and b be any two numbers satisfying $\;\large\frac{1}{a^{2}}+\large\frac{1}{b^{2}} =\large\frac{1}{4} \;$, then the foot of perpendicular from the origin on the variable line,$\;\large\frac{x}{a} + \large\frac{y}{b}=1\;$ , lies on

(a) a hyperbola with each semi - axis = $\;\sqrt{2}\;$ (b) a hyperbola with each semi - axis = 2(c) a circle of radius =2(d) a circle of radius =$\;\sqrt{2}$

the answe is surely (C)