If 5 y- 8 =0 is the equation of the directrix of a hyperbola x^2 a^2 - y^2 b^2 +1=0 and 5 2 is its eccentricity then 1a=

Step-by-step solution

x^2 a^2 - y^2 b^2 +1=0 i.e. y^2 b^2 - x^2 a^2 =1 It is conjugate hyperbola Equation of directrix must be y= b e Comparing with 5 y- 8 =0 aligned & y= 8 5 = b e & e= 5 2 aligned aligned & b= 8 5 e= 8 5 5 2 = 8 2 & b= 2 aligned e= 1+ a^2 b^2 aligned & 5 2 = 1+ a^2 2 5 4 =1+ a^2 2 & a^2 2 = 1 4 a= 1 2 aligned