Prove that the eccentricity of a rectangular hyperbola is equal to `sqrt2`.

The eccentricity of the hyperbola can never be equal to

Assertion (A): The locus of the point ((e^(2t)+e^(-2t))/(2), (e^(2t)-e^(-2t))/(2)) when 't' is a parameter represents a rectangular hyperbola. Reason (R ) : The eccentricity of a rectangular hyperbola is 2.

Statement-I A hyperbola whose asymptotes include (pi)/(3) is said to be equilateral hyperbola. Statement-II The eccentricity of an equilateral hyperbola is sqrt(2).

Prove that the perpendicular focal chords of a rectangular hyperbola are equal.

The eccentricity of the hyperbola x^(2)-y^(2)=9 is

The tangent at the point P of a rectangular hyperbola meets the asymptotes at L and M and C is the centre of the hyperbola. Prove that PL=PM=PC .

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 .

Write the eccentricity of the hyperbola 9x^2-16 y^2=144.

A triangle has its vertices on a rectangular hyperbola. Prove that the orthocentre of the triangle also lies on the same hyperbola.

A triangle has its vertices on a rectangular hyperbola. Prove that the orthocentre of the triangle also lies on the same hyperbola.