Let the tangent at any point P on a curve passing through the points 1 , 1 and 1 10 , 100 , intersect positive x -axis and y -axis at the points A and B respectively. If P A : P B = 1 : k and y = y x is the solution of the differential equation e d y d x = k x + k 2 , y 0 = k , then 4 y 1 - 5 log e 3 is equal to _______________

Step-by-step solution

Given, The tangent at any point P on a curve passing through the points 1 , 1 and 1 10 , 100 , intersect positive x -axis and y -axis at the points A and B respectively, And P   A :   P   B = 1 :   k and y = y x is the solution of the differential equation e d y d x = k x + k 2 , y 0 = k , Now on plotting the diagram we get, Equation of tangent at P x ,   y is : Y - y = dy dx X - x Coordinate of A = x - y d x d y , 0 Coordinate of B = 0 , y - x d y d x ∴    x , y = k x - k y