Let f(x)=x^2+9, g(x)= x x-9 and a =f g(10), b =g f(3) . If e and l denote the eccentricity and the length of the latus rectum of the ellipse x^2 a + y^2 b =1 , then 8 e ^2+l^2 is equal to.

Step-by-step solution

aligned & f(x)=x^2+9 g(x)= x x-9 & a=f(g(10))=f ( 10 10-9 ) & =f(10)=109 & b=g(f(3))=g(9+9) & =g(18)= 18 9 =2 & E: x^2 109 + y^2 2 =1 aligned aligned & e ^2=1- 2 109 = 107 109 & = 2(2) 109 = 4 109 & 8 e ^2+ ^2= 8(107) 109 + 16 109 & =8 aligned