1. The problem statement, all variables and given/known data For the family of curves given by (x^2)/(a^2) + (y^2)/(b^2) = 1, find the family of curves that are orthogonal to these. 2. Relevant equations Here I will number my steps 1. Differentiate 2. opposite reciprocal 3. integrate 4. simplify 3. The attempt at a solution 1. dy/dx = -(xb^2)/(ya^2) this what I have for my derivative 2. dy/dx = (ya^2)/(xb^2 ) flip and sign. 3. After integration I have (1/a^2) lny = (1/b^2)lnx 4. I just tried to simplify it So from (1/a^2) lny = (1/b^2)lnx ln(y) = (a^2/b^2)ln(x) I just got ride of ln with e. y = x^(a^2/b^2) but I feel like I should have c in my equation immediately after integration. So rather just left as it was ?