If you want to keep flow rate and pressure drop the same, because your engineering task requires it, you just have to rearrange the Hagen-Poiseuille law so that everything that is known is on the right hand side, and everything that is unknown is on the left hand side:
$$\frac{L}{r^4} = \frac{\pi\Delta P}{8\mu Q}=:C$$
Usually, you would know $C$ because you know $\Delta P$ and $Q$, and thus, you could just calculate for example the length $L$ of the pipe if you provide a reasonable pipe radius $r$.
But if you just want to know how $L$ changes if $r$ changes, in general, you can provide an 'initial guess' $(L_1,r_1)$ and eliminate the constant $C$ by equating it to a 'final set of design parameters' $(L_2,r_2)$:
$$\frac{L_2}{r_2^4}=\frac{L_1}{r_1^4}$$
Hence, if you rearrange that once again, you obtain
$$L_2=L_1\cdot\frac{r_2^4}{r_1^4}$$
In more simple words, the length of the pipe behaves like the fourth power of pipe radius, if pressure drop and current shall stay the same.
By the way, this is all reasonable and a typical engineering question. Say, you want to build a ventilation system for a building, and you need an airflow $Q$ for convenient air quality and you have found an affordable fan that provides a certain pressure drop $\Delta P$ at its maximum fan speed. Now suppose you have chosen a pipe with diameter $r$, but as soon as you calculate the length of the pipe that is compatible with your fan and ventilation requirements (like with the first equation), you notice that this pipe is not long enough (say it is 20% too short) to connect the interior of the ventilated room through the building with the outside air. Now you might well ask the question: if I increase the radius of the pipe, how much length will this gain me.
For small changes of the respective quantities, as a rule of thumb (Taylor's theorem, first order), an increase of the pipe radius of 1% will result in a permissible length increase of 4%. This is due to the power of 4 on the radius, because
$$(101\%)^4=(1.01)^4\approx 1.041\approx 104\%$$
In the example above, where the length is 20% too short, you would have to increase the pipe radius by approximately 5%. That is a pretty quick way of estimating what you need.
But of course, this is still all subject to the assumption of Hagen-Poiseuille flow.
Another caveat (if you ever have to design a ventilation system): real fans don't just offer a defined pressure drop at a certain fan speed, but the pressure drop also depends on the flow conditions around the fan, namely, if it is free blowing, or if it is placed inside a duct (which is how normally a fan is used).
