How many tangents can be drawn from a point to hyperbola?

[vkash]

y=mx+-sqrt(a²m²-b²) (which is quadratic equation)
So there should two tangents from a point but if we draw then we can even draw four tangents.
example; consider the hyperbola x²/16-y²/4=1 from point (2,0) i think four tangents can be drawn one to right side lobe and one two left one..
So which is correct equation or my analysis?

 

[vkash]

y=mx+-sqrt(a²m²-b²) (which is quadratic equation)
So there should two tangents from a point but if we draw then we can even draw four tangents.
example; consider the hyperbola x²/16-y²/4=1 from point (2,0). i think four tangents can be drawn two[/color] to right side lobe and two[/color] to left one..
So which is correct equation or my analysis?

Is this question this much tough that even after 293 views none able to reply...
I have done some type error in my first question. So please see the question written in this post.

 

[micromass]

You will only have 2 tangent lines. There will not be any tangents to the left side if you start in (2,0).

 

[vkash]

You will only have 2 tangent lines. There will not be any tangents to the left side if you start in (2,0).

Ohhhhhhh...
so that is it.