A particle is moving with velocity v=k(yi^+xj^)v = k(y\hat{i} + x\hat{j})v=k(yi^+xj^), where kkk is a constant. The general equation for its path is:
y^2 = x^2 + constant
x^2 = y^2 + constant
y = x^2 + constant
x = y^2 + constant