The area of the region bounded by hyperbola x^2-y^2=9 and its latus rectum is

Step-by-step solution

aligned & x^2-y^2=9 & a = b =1 aligned co-ordinates of latus rectum are ( a e, b^2 a )=( 3 2 , 3) Area of hyperbola and its latus rectum aligned & =4 ₃^ 3 2 y ~d x & =4 ₃^ 3 2 ( x^2-9 ) d x & =4 [ x 2 x^2-9 - 9 2 |x+ x^2-9 | ]₃^ 3 2 & =4 [ ( 3 2 2 (3 2 )^2-9 - 9 2 |3 2 + (3 2 )^2-9 | ) . & .- ( . 3 2 3^2-9 - 9 2 , 3+ 3^2-9 ) ] aligned aligned & =4 [ ( 3 2 2 3- 9 2 |3 2 +3|+ 9 2 3 ) ] & =4 [ 9 2 2 - 9 2 (3 2 +3)+ 9 2 3 ] & =4 [ 9 2 2 - 9 2 ( 3 2 +3 3 ) ] & =4 [ 9 2 2 - 9 2 ( 2 +1) ] & =4 9 2 [ 2 - ( 2 +1)] sq. units