Question

If the intercept made by the line between the axes is bisected at the point $(x_1,y_1),$ then its equation is

• A. $\frac{x}{x_1}+\frac{y}{y_1}=2$
• B. $\frac{x}{x_1}+\frac{y}{y_1}=1$
• C. $\frac{x}{x_1}+\frac{y}{y_1}=\frac{1}{2}$
• D. none of these

Answer 1

The correct option is A $\frac{x}{x_1}+\frac{y}{y_1}=2$

Let the equation be $\frac{x}{a}+\frac{y}{b}=1$

the line is bisected at the point $(x_1,y_1)$

$\Rightarrow (\frac{a}{2},\frac{b}{2})=(x_1,y_1)$

$\Rightarrow a=2x_{1}b=2y_1$

$\therefore$ Required equation is

$\frac{x}{2x_1}+\frac{y}{y_1}=1$

$\Rightarrow \frac{x}{x_1}+\frac{y}{y_1}=2$