Find the equation of hyperbola

[utkarshakash]

Homework Statement

From the point (2√2,1) a pair of tangents are drawn to [itex]\dfrac{x^2}{a^2}-\dfrac{y^2}{b^2} = 1,[/itex] which intersect the coordinate axes in concyclic points . If one of the tangents is inclined at an angle of [itex]tan^{-1}\frac{1}{√2}[/itex] with the transverse axis of the hyperbola , then find the equation of
i) hyperbola ii)circle formed using concyclic points

Homework Equations

The Attempt at a Solution

Equation of tangent
[itex]y=mx+\sqrt{a^2m^2-b^2}[/itex]
where m = [itex]tan^{-1}\frac{1}{√2}[/itex]
Passing it through the given point will give me an equation in a and b. But there are two unknowns.

 

[MrWarlock616]

Condition for tangency is ##c^2=a^2m^2-b^2##. Can you find c?

edit: sorry didn't see that you already did this. I think you have to use the fact that the points are concyclic, or find the equation of the other tangent.

 

[utkarshakash]

Condition for tangency is ##c^2=a^2m^2-b^2##. Can you find c?

edit: sorry didn't see that you already did this. I think you have to use the fact that the points are concyclic, or find the equation of the other tangent.

But how?

 

[MrWarlock616]

But how?

I think some data might be missing. All I can think of is that the slope of the tangent is -B/A where A and B represent the intercepts of this tangent. A relation between A and B can be found by looking at the circle formed by the points of the intercept, as they are at equal distances from the centre...but the centre is not known too..