Statement I The eccentricity of the hyperbola 9 x^2-16 y^2-72 x+96 y-144=0 is 5 / 4 . Statement II The eccentricity of the hyperbola x^2 a^2 - y^2 b^2 =1 is 1+ b^2 a^2

Step-by-step solution

9 x^2-16 y^2-72 x+96 y-144=0 aligned & 9 (x^2-8 x )-16 (y^2-6 y )-144=0 & 9 (x^2-8 x+16 )-16 (y^2-6 y+9 )-144 aligned -144+144=0 aligned & 9(x-4)^2-16(y-3)^2=144 & (x-4)^2 4^2 - (y-3)^2 3^2 =1 aligned Here, a=4, b=3e= 1+ b^2 a^2 = 1+ 9 16 = 5 4 Staement I and statement II are true and statement II is a correct explanation for Statement I.