If x= - , y= ¹⁰ - ¹⁰ and (x^2+4 ) ( d y d x )^2=k (y^2+4 ) , then k=

Step-by-step solution

aligned & Given, y= ¹⁰ - ¹⁰ and x= - & so, d y d =10 ( ^9 + ^9 ) & =10 ( ¹⁰ + ¹⁰ ) & and d x d = + =( + ) & d y d x =10 ¹⁰ + ¹⁰ + & ( d y d x )^2=100 ( ¹⁰ + ¹⁰ + )^2 & aligned aligned & =100 ²⁰ + ²⁰ +2 ^2 + ^2 +2 & =100 ( ¹⁰ - ¹⁰ )^2+4 ( - )^2+4 & =100 ( y^2+4 x^2+4 ) (x^2+4 ) ( d y d x )^2 & =100 (y^2+4 ) & =K (y^2+4 ) aligned (given) So, K=100