If (x - a)^2 + (y - b)^2 = c^2 , where a, b, c are some constants, c > 0 then [1 + ( dy dx )^2 ]^ 3 2 d^2y dx^2 is dependent on:

Step-by-step solution

Differentiating (x-a)^2 + (y-b)^2 = c^2 : dy dx = - x-a y-b 1 + ( dy dx )^2 = 1 + (x-a)^2 (y-b)^2 = (x-a)^2+(y-b)^2 (y-b)^2 = c^2 (y-b)^2 Differentiating again using quotient rule: d^2y dx^2 = - (y-b)^2 + (x-a)^2 (y-b)^3 = - c^2 (y-b)^3 Substituting into the expression: [1+ ( dy dx )^2 ]^ 3/2 d^2y dx^2 = ( c^2 (y-b)^2 )^ 3/2 - c^2 (y-b)^3 = c^3 (y-b)^3 - c^2 (y-b)^3 = -c The expression depends only on constant c .