Question

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

• A. $\frac{x}{x_1}+\frac{y}{y_1}=2$
• B. $2(x{y}_1+y{x}_1)=x_1{y}_1$
• C. $x{y}_1+y{x}_1=x_1{y}_1$
• D. None of these

Answer 1

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

Let x-axis intercept of line be $A(a,0)$ & y-axis intercept of line be $B(0,b)$.

Hence the equation will be:

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

According to question $(x_1,y_1)$ is mid point of $A(a,0)$ & $B(0,b)$

$\Rightarrow \frac{a+0}{2}=x_1$ & $\frac{0+b}{2}=y_1$

$\Rightarrow a=2\left(x_1\right)$ & $b=2\left(y_1\right)$

Hence the equation will be:

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

Multiplying each side by $2$ we get:

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

Ans: $\frac{x}{x_1}+\frac{y}{y_1}=2$.