Question

If points $(p,0),(0,q)$ and $(x,y)$ are collinear, then the value of $\frac{x}{p}+\frac{y}{q}$ is

Answer 1

Let the points be $P(p,0),Q(0,q)$ and $R(x,y)$.
Hence for co-linearity, the required condition is :
Slope of $PQ$ $=$ Slope of $QR$
$\Rightarrow \frac{q-0}{0-p}=\frac{y-q}{x-0}$
$\Rightarrow xq=-yp+pq\Rightarrow \frac{x}{p}+\frac{y}{q}=1$