$\begin{array}{1 1}(a)\;t_1t_2y+x=a(t_2+t_1)\\(b)\;t_1t_2x+y=a(t_2+t_1)\\(c)\;2t_1t_2y+x=a(t_2+t_1)\\(d)\;t_1t_2y+x=2a(t_2+t_1)\end{array}$

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.

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