Ok, i see there is a lot of confusions over Yoga
First, Yoga was not propogated by Hindu Gods and thus Yoga naturally lies outside the domain of Hindusim. Yoga was created by Yogis, Yogis are Saint like people.. they did not worship any kind of Idols. In simple terms,some yogis meditated on the Supreme Being, while some yogis do not even meditate on anything ..During anceint times Yogis used go to remote places where no humans can disturb them, like forests,Mountains..etc They used to meditate for years without any food, their only aim was to know "G-d" , the search for "truth". Consider a Yogi meditating and asking questions repeatedly to his inner self "Who am I, Who is controller of the World" . By continously asking questions, they used to transcend into some special realm and used to achieve supreme bliss. As meditating for years without much food and horrible climatic conditions, it was essential for them to develop certain excercises to remain fit in order to achieve their goals, This is how Physical Yoga came into being. So these excersies were deviced by these mystic men for Health reasons in their quest for spirituality.
In simple terms "Yoga" means Practise of physical or mental aspects of human beings to obtain certain goals. Yoga DOES NOT mean Exercises or Mediation alone..
Thus any person belonging to any faith is always indulging in some form of Yoga or other through various kinds of work. Hence many kinds of Yogas came into being.
Karma yoga: The yoga of action (any action good or bad)
Bhakti yoga: The yoga of devotion (Service to G-d)
Jnana yoga: The yoga of knowledge (Study of Holy books)
Hatha Yoga: The yoga of just Physical Self and/or Mental Self
Raja Yoga: The yoga of Mental Self
Pranava Yoga: The yoga of Mental Self (meditating of Aum)
Kundalini yoga: Combination of Physical,Mental and Breathing techniques. The most dangerous form of Yoga. Has to be done perfectly else its fatal, i have lost one of my relative to this. Yoga masters themself do not try this.