# Find the equation of hyperbola

1. Jan 5, 2013

### utkarshakash

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

2. Relevant equations

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

2. Jan 5, 2013

### 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.

Last edited: Jan 5, 2013
3. Jan 6, 2013

But how?

4. Jan 7, 2013

### MrWarlock616

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..