If x= - , y= ¹⁰ - ¹⁰ and (x^2+4 ) ( d y ~d x )^2= k (y^2+4 ) , then the value of k is

Step-by-step solution

aligned & x= - and y= ¹⁰ - ¹⁰ & ~d x ~d = + and & d y ~d =10 ^9 -10 ^9 (- ) aligned aligned & =10 ¹⁰ +10 ^9 & ~d y ~d x = d y ~d ~d x ~d = 10 ¹⁰ +10 ^9 + aligned = 10 ( ¹⁰ + ¹⁰ ) + aligned ( d y ~d x )^2 & = 10^2 ( ¹⁰ + ¹⁰ )^2 ( + )^2 & = 100 [ ( ¹⁰ - ¹⁰ )^2+4 ¹⁰ ¹⁰ ] ( - )^2+4 aligned aligned & ( d y d x )^2= 100 (y^2+4 ) x^2+4 & (x^2+4 ) ( d y d x )^2=100 (y^2+4 ) k =100 aligned