Review question

# Given the line $PRQ$, when is $OP + OQ$ a minimum? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R7586

## Question

The line $L$ has equation $y=c-mx$, with $m>0$ and $c>0$. It passes through the point $R(a,b)$ and cuts the axes at the points $P(p,0)$ and $Q(0,q)$, where $a$, $b$, $p$ and $q$ are all positive. Find $p$ and $q$ in terms of $a$, $b$ and $m$.

As $L$ varies with $R$ remaining fixed, show that the minimum value of the sum of the distances of $P$ and $Q$ from the origin is $(a^{\frac{1}{2}}+b^{\frac{1}{2}})^2$, and find in a similar form the minimum distance between $P$ and $Q$. (You may assume that any stationary values of these distances are minima.)