Question

If the three point $A(h,0)$, $P(a,b)$ and $B(0,k)$ lie on a line, show that :$\frac{a}{h}+\frac{b}{k}=1$.

Answer 1

It is given the point $A(h,0),B(0,b)$ and $(a,b)$ are collinear .

Therefore , slope of $PA=$ slope of $PB$

$\therefore \frac{b-0}{a-h}=\frac{b-k}{a-0}$

$\therefore ab=(a-h)(b-k)$

$\Rightarrow ab=ab-ak-bh+hk$

$\Rightarrow hk=ak+bh$

$\Rightarrow \frac{a}{h}+\frac{b}{k}=1$