Tangents are drawn to a hyperbola from a point on one of the branches of its conjugate hyperbola. Show that their chord of contact will touch the other branch of the conjugate hyperbola.

If 5/4 is the eccentricity of a hyperbola find the eccentricity of its conjugate hyperbola.

Two branches of a hyperbola

If the ecentricity of a hyperbola is sqrt3 then the ecentricity of its conjugate hyperbola is

If sec theta is the eccentricity of a hyper bola then the eccentricity of the conjugate hyperbola is

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

Tangents are drawn from the points on a tangent of the hyperbola x^2-y^2=a^2 to the parabola y^2=4a xdot If all the chords of contact pass through a fixed point Q , prove that the locus of the point Q for different tangents on the hyperbola is an ellipse.

If the eccentricity of a hyperbola is sqrt(3) , the eccentricity of its conjugate hyperbola, is

If the distance between foci of a hyperbola is twice the distance between its directrices, then the eccentricity of conjugate hyperbola is :

If the distance between foci of a hyperbola is twice the distance between its directrices, then the eccentricity of conjugate hyperbola is :

Statement-I If eccentricity of a hyperbola is 2, then eccentricity of its conjugate hyperbola is (2)/(sqrt(3)) . Statement-II if e and e_1 are the eccentricities of two conjugate hyperbolas, then ee_1gt1 .