A variable line passes through the fixed point \((\alpha, \beta)\). The locus of the foot of the perpendicular from the origin on the line is,
(A) \(x^{2}+y^{2}-\alpha x-\beta y=0\)
(B) \(x^{2}-y^{2}+2 \alpha x+2 \beta y=0\)
(C) \(\alpha x+\beta y \pm \sqrt{\left(\alpha^{2}+\beta^{2}\right)}=0\) (D)
Ans: (A)
