Question

A straight line through $P(1,2)$ is such that its intercept between the axes is bisected at P, its equation

• A. $x+2y=5$
• B. $x-y+1=0$
• C. $x+y-3=0$
• D. $2x+y-4=0$

Answer 1

The correct option is D $2x+y-4=0$

let the x-intercept be 'a' and y-intercept be 'b'

given that $(1,2)$ is the midpoint

$\Rightarrow \frac{a}{2}=1$ and $\frac{b}{2}=2$

$\Rightarrow a=2$ and $b=4$

equation of line with intercepts is : $\frac{x}{a}+\frac{y}{b}=1$

$\Rightarrow \frac{x}{2}+\frac{y}{4}=1$

$\Rightarrow 2x+y-4=0$