It is not only that you can’t run Hyper-V and HAXM simultaneously the PC has to be configured at boot to use one or the other. The problem is that Google’s Android emulator uses Intel’s HAXM (Hardware Accelerated Execution Manager) which uses the same CPU virtualization extensions as Hyper-V. If you run Windows and use the Hyper-V hypervisor, which is used by Visual Studio as well as being handy for testing stuff in virtual machines, then you will encounter an annoyance if you go on to install Android Studio, Google’s official IDE for Android. Microsoft has announced a better solution, if you are on the latest Windows 10 April 2018 Update or later, and you can now use the official Android emulator with Hyper-V.
Update: This post is out of date you may still be able to get it to work but there are stability issues with the emulator.