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

Comparison of Hyperbola and its conjugate hyperbola

A hyperbola and its conjugate have the same assymptote and The equation of the pair of assymptotes differ from the equation of hyperbola and the conjugate hyperbola by some constant only.

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

If a,b are eccentricities of a hyperbola and its conjugate hyperbola then a^(-2)+b^(-2)=

If a,b are eccentricities of a hyperbola and its conjugate hyperbola then a^(-2)+b^(-2)=

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.

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.

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.

From a point P, tangents are drawn to the hyperbola 2xy = a^(2) . If the chord of contact of these tangents touches the rectangular hyperbola x^(2) - y^(2) = a^(2) , prove that the locus of P is the conjugate hyperbola of the second hyperbola.