If the line `(x)/(b) + (y)/(b) = 1` moves in such a way that `(1)/(a_(2)) + (1)/(b_(2)) = (1)/(c_(2))`, where c is a constant, then prove that the foot of perpendicular from the origin upon the straight line describes the curve
`x^(2) + y(2) = c^(2).`