If (a+ 2 b x)(a- 2 b y)=a^2-b^2 , where a b 0 , then d x ~d y at ( 4 , 4 ) is

Step-by-step solution

(a+ 2 b x)(a- 2 b y)=a^2-b^2 Differentiating both sides w.r.t. y , we get aligned & aligned &( a + 2 ~b x)( 2 ~b y) & +( a - 2 ~b y) (- 2 ~b x ~d x ~d y )=0 & ~d x ~d y = 2 ~b y( a + 2 ~b x) 2 ~b x( a - 2 ~b y) & ( d x ~d y )_ ( 4 4 ) = b ( a + b ) b ( a - b ) = a + b a - b aligned aligned