Question

A line passes through the point (3,-2). Find the locus of the middle point of the portion of the line intercepted between the axis.

Answer 1

Equation of line with mid-point $(n,k)$ of the portion of line between the axes.

$\frac{x}{2n}+\frac{y}{2x}=1$ (equation in form of intercepts)

as this line passes through $(-3,2)$

$\frac{-3}{2n}+\frac{2}{2k}=1$

$-3k+4h=4kh$

$4h-3k-4kh=0$

$4x-3y-4xy=0$ (This is the required loues).