 Good morning friends, I am Purva and today we will work out the following question. Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b and we have x upon a plus y upon b is equal to 1. Now as the order of a differential equation representing a family of curve is same as the number of arbitrary constants present in the equation corresponding to the family of curves so here we shall differentiate the equation two times. So this is the key idea behind our question. Let us now begin with the solution. So here we are given x upon a plus y upon b is equal to 1. Let us mark this as equation 1. Now since the above equation consists of two arbitrary constants so for eliminating them we shall differentiate equation one two times. So differentiating 1 with respect to x we get, differentiating x upon a with respect to x we get, 1 upon a plus differentiating y upon b with respect to x we get, 1 upon b into dy by dx is equal to differentiating 1 with respect to x we get, 0. This implies 1 upon a plus 1 upon b into, now dy by dx can be written as y dash is equal to 0 and this can also be written as this implies 1 upon b into y dash is equal to minus 1 upon a which further implies y dash is equal to minus b upon a and we mark this as equation 2. Now differentiating equation 2 with respect to x we get, differentiating y dash with respect to x we get y double dash is equal to differentiating minus b upon a with respect to x gives 0 so we get y double dash is equal to 0. And this equation does not contain the constants a and b therefore the required differential equation is y double dash is equal to 0. Hence we write our answer as y double dash is equal to 0, hope you have understood the solution, bye and take care.