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 to right side lobe and two 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.

 

[CellCoree]

Your analysis is correct. The number of tangents that can be drawn from a point to a hyperbola depends on the position of the point relative to the hyperbola. In some cases, there may be two tangents, while in others there may be four. So, both the equation and your analysis are correct.