Hyperbola · Mathematics · BITSAT

The locus of the mid-point of the chords of the circle $x^2+y^2=16$ which are tangents to the hyperbola $9 x^2-16 y^2=144$ is $\left(x^2+y^2\right)^2=k x^2-l y^2$. Then, the sum of values of $k$ and $l$ is

If x = 9 is the chord of contact of the hyperbola x² $$-$$ y² = 9, then the equation of the corresponding pair of tangent is