Question

Find the equation of line whose intercept by the axes is bisected at the point $(x_1,y_1)$.

Answer 1

A(a, 0) , B(0,b),

mid - point of AB is (a/2 , b/2) = $(x_1,y_1)$ is given
$\therefore a=2x_1,b=2y_1\therefore linesis\frac{x}{a}+\frac{y}{b}=1$
or $\frac{x}{2x_1}+\frac{y}{2y_1}=1$ or $x{y}_1+y{x}_1=2x_1{y}_1$