Question

Find the equation to the straight line which passes through the given point $(x^{\prime },y^{\prime })$ and is such that the given point bisects the part intercepted between the axes.

Answer 1

As $x^{\prime }=\frac{a}{2}$ and $y^{\prime }=\frac{b}{2}$

$\Rightarrow a=2x^{\prime }$ & $b=2y^{\prime }$

Then,

$\frac{x}{a}+\frac{y}{b}=1$

$\Rightarrow \frac{x}{2x^{\prime }}+\frac{y}{2y^{\prime }}=1$

$\Rightarrow \frac{x}{x^{\prime }}+\frac{y}{y^{\prime }}-2=0$

$\Rightarrow x{y}^{\prime }+y{x}^{\prime }=2x^{\prime }{y}^{\prime }$ is the required equation