Equation of line will be
$(y-\large\frac{a}{t_1})=\frac{\Large\frac{a}{t_2}-\frac{a}{t_1}}{a(t_2-t_1)}$$(x-at_1)$
$(y-\large\frac{a}{t_1})=\frac{a(t_1-t_2)(x-at_1)}{t_2t_1\times a(t_2-t_1)}$
$(y-\large\frac{a}{t_1})=\frac{-1(x-at_1)}{t_1t_2}$
$(y-\large\frac{a}{t_1})=\large\frac{a}{t_2}-\frac{x}{t_1t_2}$
$y+\large\frac{x}{t_1t_2}=\frac{a(t_2+t_1)}{t_2t_1}$
$t_1t_2y+x=a(t_2+t_1)$
This equation is also known as parametric equation of line.
Hence (a) is the correct answer.