If the eccentricity of the hyperbola ( x² a² - y² b² =1 ) is ( 5 4 ) and ( 2 x+3 y-6=0 ) is a focal chord of the hyperbola, then the length of transverse axis is equal to

Step-by-step solution

Given equation of hyperbola, [ x² a² - y² b² =1 (1) ] and a focal chord of the hyperbola is, [ 2 x+3 y-6=0 (2) ] We know that, focus is given by ( (a e, 0) . ) So, from Eq. (2) we have [ 2 a e-6=0 a e=3 a= 3 e ] [ array l Hence e= 5 4 then, a= 3 5 / 4 = 12 5 array ] Length of the transverse axis is ( 2 a . ) So, ( 2 a= 24 5 )