Prove that chords of a hyperbola, which touch the conjugate hyperbola, are bisected at the point of contact.

Prove that in two concentric circles, the chord of the larger circle which touches the smaller circle is bisected at the point of contact.

In two concentric circle,prove that a chord of larger circle which is tangent to smaller circle is bisected at the point of contact.

Prove that in two concentric circles,the chord of the larger circle,which touches,the smaller circle,is bisected at the point of contact.

Comparison of Hyperbola and its conjugate hyperbola

Prove that any hyperbola and its conjugate hyperbola cannot have common normal.

The equation of the chord of the hyperbola xy=c^(2), which is bisected at the point (2c,3c) is