Short answer

Now Youtube offers more options for live streaming. You could still use Hangouts on Air but also could use the Stream Now [BETA], but if you still want to use Hangouts on Air, you will require a Google+ profile or Google+ page.

Extended answer

Hangouts on Air requires a Google+ profile or Google+ page connected to a Youtube Channel. It's worth to say that

1. Now are other options for live streaming from a Youtube channel.
2. Youtube is making changes so will not be required anymore a Google+ profile or page to be tied to a Youtube channel.

Regarding 1, now there are three types of doing live streaming in Youtube: Stream now Beta, Quick and Custom Live Event.

Regarding 2, from Your channel and Google+ - Youtube Help

Most people don't need Google+ to use YouTube.

If you’re comfortable using the name and photo you’ve selected for your Google account on YouTube, you no longer need to have a Google+ profile on your account. You can create a channel and use all YouTube features without Google+. If you already have a Google+ profile, it won't affect your channel whether you keep or remove your Google+ profile.

Reasons you might still need Google+ connected to your YouTube channel

• If you want to use a different name and photo on YouTube than the name and photo you’ve chosen for your Google account, your channel should be connected to a Google+ page. When connected to a Google+ page, your YouTube channel gets its name and channel icon from the connected page, instead of from your Google account. Any name and photo changes will apply to both the Google+ page and the YouTube channel.

• If you want multiple managers to have access to your channel without sharing passwords, you can use admin features with a Google+ page.

You’ll soon be able to do the above without Google+ Pages as well. Check out our blog post for more information and keep an eye on this article for updates.

Comment notifications

If you want to get comment notifications through the notification bell , your account needs to have an associated Google+ profile or page.

What if I never connected my channel to Google+?

If you’d like to use the same name and photo that you’ve selected for your Google account on YouTube, consider confirming your name so you can regain some features on YouTube, like commenting.

References

• Now you can live stream on YouTube - Youtube Creators Blog
• Get started with Hangouts On Air - Classic Google+ Help
• Introduction to Live Streaming - Youtube Help
• Stream now Beta, Quick and Custom Live Event Types

Unfortunately, no. There is currently no way to do a private stream on Twitch.

As an alternative, you could use YouTube to host your private livestream.