1. The problem statement, all variables and given/known data Show that the families (x+c1)(x2+y2)+x = 0 and (y+c2)(x2+y2)-y = 0 2. Relevant equations For the 2 curves to be orthogonal their slopes should be negative recriprocles. 3. The attempt at a solution I'm pretty sure that for the first set of curves: y'(x) = - (2c1 x + 3x2+y[x]2+1)/(2(c1+x)y[x]) and for the second set of curves: y'(x) = (2x (c2 +y)) / (2c2 y[x] + x2 + 3y[x]2-1) which are not negative recriprocles of each other. I'm thinking i went wrong somewhere along the lines of finding the deravitive. if anyone could please help me out i'd really appreciate it. I used Mathematica to get those answers: For the first set i factored out the original problem then took the deravitive of that: D[c1 x^2 + c1 y[x]^2 + x^3 + x y[x]^2 + x, x] then i used the solve command to solve that for y'[x] For the second set i factored out the original problem, then took the deravitive of that with respect to x: D[c2 x^2 + c2 y[x]^2 + x^2 y[x] + y[x]^3 - y[x], x] Then i used the Solve function to solve that for y'[x] P.S. I'm pretty sure these are supposed to be orthogonal just because there isn't an option for not orthogonal. Like i said any help would be appreciated.