Question

If the line $px-qy=r$ intersects the co-ordinate axes at (a,0) and (0,b), then value of a+b is equal to

• A. $r\left(\frac{q+p}{qp}\right)$
• B. $r\left(\frac{q-p}{pq}\right)$
• C. $r\left(\frac{p-q}{pq}\right)$
• D. $r\left(\frac{p+q}{p-q}\right)$
• E. $r\left(\frac{p-q}{p+q}\right)$

Answer 1

Answer: (B)

$r\left(\frac{q-p}{pq}\right)$

$px-qy=r\Rightarrow \frac{x}{\left(r/p\right)}-\frac{y}{\left(r/q\right)}=1$

(Interept form)

$a=\frac{r}{p},b=-\frac{-r}{q}$

$r(\frac{1}{p}-\frac{1}{q})=a+b\Rightarrow r\frac{(q-p)}{pq}$