Let (x, y) be such that ⁻¹(a x)+ ⁻¹(y)+ ⁻¹(b x y)= 2 . Match the statements in Column I with the values in Column II.

Step-by-step solution

(A) If a=1 and b=0 , then ⁻¹ x+ ⁻¹ y=0 ⁻¹ x=- ⁻¹ y x^2+y^2=1 (B) If a=1 and b=1 , then array rlrl & & ⁻¹ x+ ⁻¹ y+ ⁻¹ x y & = 2 & & ⁻¹ x- ⁻¹ y & = ⁻¹ x y & x y+ 1-x^2 1-y^2 & =x y [taking sine on both the sides] array (C) If a=1 and b=2 , then aligned & & ⁻¹ x+ ⁻¹ y+ ⁻¹(2 x y) & = 2 & & ⁻¹ x- ⁻¹ y & = ⁻¹(2 x y) & & x y+ 1-x^2 1-y^2 & =2 x y & & x^2+y^2 & =1 aligned [on squaring] (D) If a=2 and b=2 , then aligned & & ⁻¹(2 x)+ ⁻¹(y)+ ⁻¹(2 x y) & = 2 & & 2 x y+ 1+4 x^2 1-y^2 & =2 x y & & (4 x^2-1 ) (y^2-1 ) & =0 . alig