Question

P(a, b) is the mid point of a line segmen between axis. Show that equation of the line is $\frac{x}{a}+\frac{y}{b}=2$

Answer 1

Let A(x, 0) and B(0, y) be two points where the line intersect x and y-axes respectively and P(a, b) is mid point of AB.

Then

$\frac{0+x}{2}=a\Rightarrow x=2a$

and $\frac{0+y}{2}=b\Rightarrow y=2b$

Now equation of required line is

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