If a directrix of a hyperbola centred at the origin and passing through the point (4,-2 3 ) is 5 x=4 and e is its eccentricity, then e^2=

Step-by-step solution

Since hyperbola x^2 a^2 - y^2 b^2 =1 passes through (4,-2 3 ) 16 a^2 - 12 b^2 =1 16-12 a^2 b^2 =a^2 ... (i) Directrix : 5 x=4 4 5 = a e 16 e^2=5 a^2 ... (ii) From eq. (i) and (ii), aligned & 16- 12 e^2-1 = 16 e^2 5 4 e^4-24 e^2+35=0 & e^2= 7 2 , 5 2 aligned