Is this covering problem NP-hard?

Given a rectangular region $R$ and a set $D$ of $n$ disks such that the union of all disks in $D$ cover the entire rectangular region $R$, the objective is to find the minimum cardinality set $D'$ subset of $D$ such that the union of all disks in $D'$ cover the entire $R$. I believe that this problem is NP-hard, but did not find any reference. can somebody help me to find the one or reduction from an NP-hard problem.

Then, if there is a solution to an instance of 3-SAT, there is a set $D'$ that for each And-gadget covers either terminal $A$ or $C$, but never both. And in which the gaps that are part of wires are covered exactly once. Hence, such cover is optimal.
Conversely, if no solution exists, some wire needs more disks to cover, or some And-gadget is covered by both terminal $A$ and $C$, requiring a higher cardinality cover.