The eccentricity of a rectangular hyperbola is

Step-by-step solution

The general equation of a hyperbola is ( x^2 a^2 - y^2 b^2 =1 ), where (a ) represents the transverse of hyperbola and (b ) represents the conjugate of the hyperbola. The eccentricity of a hyperbola is (e= a^2+b^2 a (1) ). Since a rectangular hyperbola is defined as a hyperbola whose transverse axis is identical to its conjugate axis, (a=b ). Substitute (a=b ) into (1). ( aligned & e= a^2+b^2 a & e= a^2+a^2 a & e= 2 a^2 a & e= 2 a a & e= 2 aligned )