A hyperbola and its conjugate have the same asymptotes

Statement-I A hyperbola and its conjugate hyperbola have the same asymptotes. Statement-II The difference between the second degree curve and pair of asymptotes is constant.

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

If e_(1) and e_(2) are the eccentricities of the hyperbola and its conjugate hyperbola respectively then (1)/(e_(1)^(2))+(1)/(e_(2)^(2)) is equal to

From any point of the hyperbola x^(2)/a^(2)-y^(2)/b^(2)=1 , tangents are drawn to another hyperbola which has the same asymptotes. Show that the chord of con- tact cuts off a constant area from the asymptotes.

If e and e' the eccentricities of a hyperbola and its conjugate,prove that (1)/(e^(2))+(1)/(e^(2))=1

Find the asymptotes of the hyperbola 2x^2+5xy+2y^2+4x+5y=0 . Find also the general equation of all the hyperbolas having the same set of asymptotes.

The chord of contact of a point P w.r.t a hyperbola and its auxiliary circle are at right angle.Then the point P lies on conjugate hyperbola one of the directrix one of the asymptotes (d) none of these