Question

If a straight line passing through $\left(x_1,y_1\right)$ and its segment between the axes is bisected at this point, then its equation is given by

• A. $\frac{x}{x_1}+\frac{y}{y_1}=1$
• B. $\frac{x}{x_1}+\frac{y}{y_1}=2$
• C. $x{y}_1+y{x}_1=1$
• D. $2\left(x{y}_1+y{x}_1\right)=x_1{y}_1$

Answer 1

Answer: (B)

Let $x$ and $y$ intercept are $a$ and $b$

$\therefore x_1=\frac{0+a}{2}\Rightarrow a=2x_1$ and
$y_1=\frac{0+b}{2}\Rightarrow b=2y_1$
$\therefore$ Equation of line is $\frac{x}{a}+\frac{y}{b}=1$
$\therefore \frac{x}{2x_1}+\frac{y}{2y_1}=1\Rightarrow \frac{x}{x_1}+\frac{y}{y_1}=2$