since upgrading to yosemite my MacBook Pro want detect my external display

Which model MacBook Pro do you have (e.g., "15-inch Late 2011") and which model is your external display? How is it connected to your MacBook Pro?

Call back,

Clinton

MacBook Pro (15” Late 2011), OS X Yosemite 10.10, 16GB Crucial RAM, 960GB M500 Crucial SSD, 27” Apple Thunderbolt Display

And you've a Thunderbolt/Mini DisplayPort to HDMI adapter connecting the Acer monitor to your computer? What make and model is your adapter? It could be the adapter that's not compatible, although it's certainly possible that the system software did a number on your connection. If you connect the Acer display, does it show up in System Preferences>Displays pane?

Call back,

Clinton

MacBook Pro (15” Late 2011), OS X Yosemite 10.10, 16GB Crucial RAM, 960GB M500 Crucial SSD, 27” Apple Thunderbolt Display

And you've not changed the set-up since upgrading to Yosemite? Certain that the adapter is plugged into the Thunderbolt port? Have you tried another HDMI cable or is the adapter an "all-in-one" Thunderbolt to HDMI cable?

Clinton

MacBook Pro (15” Late 2011), OS X Yosemite 10.10, 16GB Crucial RAM, 960GB M500 Crucial SSD, 27” Apple Thunderbolt Display

I have the same issue, It worked perfectly on Mavericks, so I doubt it is a hardware problem. After the Yosemite installation, my MacBook Air 13 inch Mid 2013 model won't detect the TV display anymore. I'm using an all-in-one Thunderbolt to HDMI cable. I've tried SMC reset, PRAM/NVRAM reset to no avail.

The display won't show up in Display preferences. But when I plug the cable in, the screen blinks but the resolution does not change. When unplugged, it does the same thing.

I am also having this issue on my MacBook Pro (15-inch, mid-2010). Since I installed Yosemite I can no longer use my ViewSonic HDMI monitor connected to the Mini Display Port. When I connect the plug to the laptop there is a screen flash, but it doesn't go to the next step and bring up the second monitor. It gives the impression that something might be crashing or failing.

I have a second partition with Mavericks on the same laptop, and the HDMI monitor works fine when I run that system. So it's not the SMC or the PRAM, but something about OS X Yosemite that is preventing the monitor from working. I have reset both the SMC and the PRAM to make sure.

As I look around my Console log, I see some references to com.apple.AmbientDisplayAgent ("AMBD Agent: xpc connection became invalid during event handler.") and there are some posts on MacRumors that seem to implicate this same Apple service.

It's possible on my system that some display-related add-ons are incompatible with Yosemite. I have the apps "Stay" and "SizeUp" and I may try disabling them next. But I don't believe I have any display-related kernel extensions or anything like that. I have some extra drives, so I might try a completely fresh install of Yosemite also...

Same issue with my 13 inch MacBook Pro (mid-2010) with Griffin MiniDisplayPort to DVI adapter. Had worked fine for years with Mavericks and previous, and even with Yosemite up until this morning. Then same issue as you - when plug in monitor there's a momentary screen blink like there always was, but then no recognition of an external monitor.

I never had any display-related add-ons like you say you do, and I still have this issue - so I bet your add-ons have nothing to do with it.

Anybody find a fix for this yet?

Here's an Apple Discussions thread that might help. It suggests using Disk Utility to repair permissions to fix the following issue, which I just found on my system:

User differs on “private/var/db/displaypolicyd”; should be 0; user is 244.

Group differs on “private/var/db/displaypolicyd”; should be 0; group is 244.

If Repair Permissions doesn't do the trick (because it doesn't stick across sleep and restarts), helpful user "lplacencia" has provided some Terminal commands to patch up the files as needed. With any luck a 10.10.1 update will address this soon!

I haven't had a chance to test this fix yet, but I will do so later tonight. Meanwhile I can report that booting up in Safe Mode didn't make any difference for me. My system includes MacPorts (which includes some running services) so I might need to eliminate that factor, if Disk Utility doesn't help.

A total clean install would have to be my next step. (And I might try that anyway just to see if it's a problem in Yosemite generally.) It's not possible to download the Yosemite full installer from Apple through a public website, but you can save the installer and use it to re-install without having to download it again.

Good news! I'm not sure what you mean by "updated last bug fix." What did you do to cure the issue?

I have tried Disk Utility to repair permissions and this didn't help me. And I have never been able to determine what the messages in Console mean. I just updated another MacBook to Yosemite and it can no longer connect to the external HDMI screen either, so I'm even more anxious to find a cure that works for us.