The line pair joining the origin to the points A and B of intersection of the conic $\displaystyle ax^2+by^2=1$ and $\displaystyle lx+my=1$ is

$\displaystyle (a-l^2)x^2-2lmxy+(b-m^2)y^2=0$

If angle AOB is a right angle, show that AB touches the circle

$\displaystyle (a+b)(x^2+y^2)=1$

I have no idea how to do this. Any pointers?

Thanks a million!